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JEE Main
Quadratic Equation and Inequalities
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Let $$\alpha, \beta(\alpha>\beta)$$ be the roots of the quadratic equation $$x^{2}-x-4=0 .$$ If $$P_{n}=\alpha^{n}-\beta...
JEE Main 2022 (Online) 29th July Evening Shift
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The sum of all real values of $$x$$ for which $$\frac{3 x^{2}-9 x+17}{x^{2}+3 x+10}=\frac{5 x^{2}-7 x+19}{3 x^{2}+5 x+12...
JEE Main 2022 (Online) 28th July Morning Shift
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The number of distinct real roots of the equation $$x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right...
JEE Main 2022 (Online) 26th July Morning Shift
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If for some $$\mathrm{p}, \mathrm{q}, \mathrm{r} \in \mathbf{R}$$, not all have same sign, one of the roots of the equat...
JEE Main 2022 (Online) 26th July Morning Shift
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Let for $$f(x) = {a_0}{x^2} + {a_1}x + {a_2},\,f'(0) = 1$$ and $$f'(1) = 0$$. If a0, a1, a2 are in an arithmatico-geomet...
JEE Main 2022 (Online) 30th June Morning Shift
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Let p and q be two real numbers such that p + q = 3 and p4 + q4 = 369. Then $${\left( {{1 \over p} + {1 \over q}} \right...
JEE Main 2022 (Online) 26th June Evening Shift
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The sum of the cubes of all the roots of the equation $${x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0$$ is _________....
JEE Main 2022 (Online) 26th June Morning Shift
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If the sum of all the roots of the equation $${e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0$$ is $${\log _e}p$$...
JEE Main 2022 (Online) 27th June Morning Shift
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Let $$\alpha$$, $$\beta$$ be the roots of the equation $${x^2} - 4\lambda x + 5 = 0$$ and $$\alpha$$, $$\gamma$$ be the ...
JEE Main 2022 (Online) 27th June Evening Shift
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The number of real solutions of the equation $${e^{4x}} + 4{e^{3x}} - 58{e^{2x}} + 4{e^x} + 1 = 0$$ is ___________....
JEE Main 2022 (Online) 28th June Morning Shift
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Let f(x) be a polynomial of degree 3 such that $$f(k) = - {2 \over k}$$ for k = 2, 3, 4, 5. Then the value of 52 $$-$$ ...
JEE Main 2021 (Online) 1st September Evening Shift
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Let $$\lambda$$ $$\ne$$ 0 be in R. If $$\alpha$$ and $$\beta$$ are the roots of the equation x2 $$-$$ x + 2$$\lambda$$ =...
JEE Main 2021 (Online) 26th August Evening Shift
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The sum of all integral values of k (k $$\ne$$ 0) for which the equation $${2 \over {x - 1}} - {1 \over {x - 2}} = {2 \o...
JEE Main 2021 (Online) 26th August Morning Shift
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If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a4 + b4 + c4 is equal to ______________....
JEE Main 2021 (Online) 25th July Evening Shift
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The number of real roots of the equation e4x $$-$$ e3x $$-$$ 4e2x $$-$$ ex + 1 = 0 is equal to ______________....
JEE Main 2021 (Online) 27th July Evening Shift
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If $$\alpha$$, $$\beta$$ are roots of the equation $${x^2} + 5(\sqrt 2 )x + 10 = 0$$, $$\alpha$$ > $$\beta$$ and $${P...
JEE Main 2021 (Online) 25th July Morning Shift
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The number of solutions of the equation $${\log _{(x + 1)}}(2{x^2} + 7x + 5) + {\log _{(2x + 5)}}{(x + 1)^2} - 4 = 0$$, ...
JEE Main 2021 (Online) 20th July Evening Shift
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Let $$\alpha$$ and $$\beta$$ be two real numbers such that $$\alpha$$ + $$\beta$$ = 1 and $$\alpha$$$$\beta$$ = $$-$$1. ...
JEE Main 2021 (Online) 26th February Evening Shift
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The sum of 162th power of the roots of the equation x3 $$-$$ 2x2 + 2x $$-$$ 1 = 0 is ________....
JEE Main 2021 (Online) 26th February Morning Shift
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The number of solutions of the equation log4(x $$-$$ 1) = log2(x $$-$$ 3) is _________.
JEE Main 2021 (Online) 26th February Morning Shift
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The number of the real roots of the equation $${(x + 1)^2} + |x - 5| = {{27} \over 4}$$ is ________.
JEE Main 2021 (Online) 24th February Evening Slot
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The least positive value of 'a' for which the equation 2x2 + (a – 10)x + $${{33} \over 2}$$ = 2a has real roots is...
JEE Main 2020 (Online) 8th January Morning Slot
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MCQ (Single Correct Answer)
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If $$\frac{1}{(20-a)(40-a)}+\frac{1}{(40-a)(60-a)}+\ldots+\frac{1}{(180-a)(200-a)}=\frac{1}{256}$$, then the maximum val...
JEE Main 2022 (Online) 29th July Morning Shift
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Let $$\alpha$$, $$\beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+\sqrt{6}=0$$ and $$\frac{1}{\alpha^{2}}+1, \fr...
JEE Main 2022 (Online) 28th July Evening Shift
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If $$\alpha, \beta$$ are the roots of the equation $$ x^{2}-\left(5+3^{\sqrt{\log _{3} 5}}-5^{\sqrt{\log _{5} 3}}\right)...
JEE Main 2022 (Online) 27th July Evening Shift
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The minimum value of the sum of the squares of the roots of $$x^{2}+(3-a) x+1=2 a$$ is:
JEE Main 2022 (Online) 26th July Evening Shift
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Let S be the set of all integral values of $$\alpha$$ for which the sum of squares of two real roots of the quadratic eq...
JEE Main 2022 (Online) 30th June Morning Shift
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If the sum of the squares of the reciprocals of the roots $$\alpha$$ and $$\beta$$ of the equation 3x2 + $$\lambda$$x $$...
JEE Main 2022 (Online) 24th June Morning Shift
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The number of distinct real roots of the equation x7 $$-$$ 7x $$-$$ 2 = 0 is
JEE Main 2022 (Online) 24th June Evening Shift
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The sum of all the real roots of the equation $$({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$$ is
JEE Main 2022 (Online) 24th June Evening Shift
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Let a, b $$\in$$ R be such that the equation $$a{x^2} - 2bx + 15 = 0$$ has a repeated root $$\alpha$$. If $$\alpha$$ and...
JEE Main 2022 (Online) 25th June Evening Shift
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The number of distinct real roots of x4 $$-$$ 4x + 1 = 0 is :
JEE Main 2022 (Online) 27th June Morning Shift
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The number of real solutions of $${x^7} + 5{x^3} + 3x + 1 = 0$$ is equal to ____________.
JEE Main 2022 (Online) 28th June Morning Shift
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Let f(x) be a quadratic polynomial such that f($$-$$2) + f(3) = 0. If one of the roots of f(x) = 0 is $$-$$1, then the s...
JEE Main 2022 (Online) 28th June Evening Shift
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Let $$\alpha$$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $$\alpha$$1011 + $$\alpha$$2022 $$-$$ $$\al...
JEE Main 2022 (Online) 29th June Evening Shift
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The numbers of pairs (a, b) of real numbers, such that whenever $$\alpha$$ is a root of the equation x2 + ax + b = 0, $$...
JEE Main 2021 (Online) 1st September Evening Shift
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The sum of the roots of the equation $$x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0$$, is :
JEE Main 2021 (Online) 31st August Evening Shift
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cosec18$$^\circ$$ is a root of the equation :
JEE Main 2021 (Online) 31st August Morning Shift
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The set of all values of K > $$-$$1, for which the equation $${(3{x^2} + 4x + 3)^2} - (k + 1)(3{x^2} + 4x + 3)(3{x^2}...
JEE Main 2021 (Online) 27th August Evening Shift
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Let $$\alpha$$, $$\beta$$ be two roots of the equation x2 + (20)1/4x + (5)1/2 = 0. Then $$\alpha$$8 + $$\beta$$8 is equa...
JEE Main 2021 (Online) 27th July Morning Shift
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The number of real solutions of the equation, x2 $$-$$ |x| $$-$$ 12 = 0 is :
JEE Main 2021 (Online) 25th July Evening Shift
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Let $$\alpha = \mathop {\max }\limits_{x \in R} \{ {8^{2\sin 3x}}{.4^{4\cos 3x}}\} $$ and $$\beta = \mathop {\min }\li...
JEE Main 2021 (Online) 27th July Evening Shift
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The number of real roots of the equation $${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$$ is :
JEE Main 2021 (Online) 25th July Morning Shift
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If $$\alpha$$ and $$\beta$$ are the distinct roots of the equation $${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$$, then the va...
JEE Main 2021 (Online) 20th July Morning Shift
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The value of $$3 + {1 \over {4 + {1 \over {3 + {1 \over {4 + {1 \over {3 + ....\infty }}}}}}}}$$ is equal to
JEE Main 2021 (Online) 18th March Morning Shift
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Let $$\alpha$$, $$\beta$$, $$\gamma$$ be the real roots of the equation, x3 + ax2 + bx + c = 0, (a, b, c $$\in$$ R and a...
JEE Main 2021 (Online) 18th March Morning Shift
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The value of $$4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}$$ is :
JEE Main 2021 (Online) 17th March Morning Shift
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Let $$\alpha$$ and $$\beta$$ be the roots of x2 $$-$$ 6x $$-$$ 2 = 0. If an = $$\alpha$$n $$-$$ $$\beta$$n for n $$ \ge ...
JEE Main 2021 (Online) 25th February Evening Shift
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The integer 'k', for which the inequality x2 $$-$$ 2(3k $$-$$ 1)x + 8k2 $$-$$ 7 > 0 is valid for every x in R, is :...
JEE Main 2021 (Online) 25th February Morning Slot
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Let p and q be two positive numbers such that p + q = 2 and p4+q4 = 272. Then p and q are roots of the equation :...
JEE Main 2021 (Online) 24th February Morning Slot
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If $$\alpha $$ and $$\beta $$ are the roots of the equation 2x(2x + 1) = 1, then $$\beta $$ is equal to :
JEE Main 2020 (Online) 6th September Evening Slot
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If $$\alpha $$ and $$\beta $$ be two roots of the equation x2 – 64x + 256 = 0. Then the value of $${\left( {{{{\alpha ^3...
JEE Main 2020 (Online) 6th September Morning Slot
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If $$\alpha $$ and $$\beta $$ are the roots of the equation, 7x2 – 3x – 2 = 0, then the value of $${\alpha \over {1 - {...
JEE Main 2020 (Online) 5th September Evening Slot
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The product of the roots of the equation 9x2 - 18|x| + 5 = 0 is :
JEE Main 2020 (Online) 5th September Morning Slot
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Let $$\lambda \ne 0$$ be in R. If $$\alpha $$ and $$\beta $$ are the roots of the equation, x2 - x + 2$$\lambda $$ = 0...
JEE Main 2020 (Online) 4th September Evening Slot
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Let $$\alpha $$ and $$\beta $$ be the roots of x2 - 3x + p=0 and $$\gamma $$ and $$\delta $$ be the roots of x2 - 6x + q...
JEE Main 2020 (Online) 4th September Morning Slot
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Let [t] denote the greatest integer $$ \le $$ t. Then the equation in x, [x]2 + 2[x+2] - 7 = 0 has :
JEE Main 2020 (Online) 4th September Morning Slot
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The set of all real values of $$\lambda $$ for which the quadratic equations, ($$\lambda $$2 + 1)x2 – 4$$\lambda $$x +...
JEE Main 2020 (Online) 3rd September Evening Slot
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If $$\alpha $$ and $$\beta $$ are the roots of the equation x2 + px + 2 = 0 and $${1 \over \alpha }$$ and $${1 \over \b...
JEE Main 2020 (Online) 3rd September Morning Slot
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Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root...
JEE Main 2020 (Online) 2nd September Evening Slot
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Let $$\alpha $$ and $$\beta $$ be the roots of the equation 5x2 + 6x – 2 = 0. If Sn = $$\alpha $$n + $$\beta $$n, n = 1...
JEE Main 2020 (Online) 2nd September Morning Slot
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Let a, b $$ \in $$ R, a $$ \ne $$ 0 be such that the equation, ax2 – 2bx + 5 = 0 has a repeated root $$\alpha $$, which ...
JEE Main 2020 (Online) 9th January Evening Slot
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The number of real roots of the equation, e4x + e3x – 4e2x + ex + 1 = 0 is :...
JEE Main 2020 (Online) 9th January Morning Slot
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Let $$\alpha = {{ - 1 + i\sqrt 3 } \over 2}$$. If $$a = \left( {1 + \alpha } \right)\sum\limits_{k = 0}^{100} {{\alpha ...
JEE Main 2020 (Online) 8th January Evening Slot
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Let S be the set of all real roots of the equation, 3x(3x – 1) + 2 = |3x – 1| + |3x – 2|. Then S :...
JEE Main 2020 (Online) 8th January Evening Slot
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Let $$\alpha $$ and $$\beta $$ be the roots of the equation x2 - x - 1 = 0. If pk = $${\left( \alpha \right)^k} + {\l...
JEE Main 2020 (Online) 7th January Evening Slot
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Let $$\alpha $$ and $$\beta $$ be two real roots of the equation (k + 1)tan2x - $$\sqrt 2 $$ . $$\lambda $$tanx = (1 - k...
JEE Main 2020 (Online) 7th January Morning Slot
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If $$\alpha $$, $$\beta $$ and $$\gamma $$ are three consecutive terms of a non-constant G.P. such that the equations $$...
JEE Main 2019 (Online) 12th April Evening Slot
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The number of real roots of the equation 5 + |2x – 1| = 2x (2x – 2) is
JEE Main 2019 (Online) 10th April Evening Slot
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If $$\alpha $$ and $$\beta $$ are the roots of the quadratic equation, x2 + x sin $$\theta $$ - 2 sin $$\theta $$ = 0, ...
JEE Main 2019 (Online) 10th April Morning Slot
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All the pairs (x, y) that satisfy the inequality $${2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}...
JEE Main 2019 (Online) 10th April Morning Slot
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If m is chosen in the quadratic equation (m2 + 1) x2 – 3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, ...
JEE Main 2019 (Online) 9th April Evening Slot
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Let p, q $$ \in $$ R. If 2 - $$\sqrt 3$$ is a root of the quadratic equation, x2 + px + q = 0, then :
JEE Main 2019 (Online) 9th April Morning Slot
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The number of integral values of m for which the equation (1 + m2 )x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is :...
JEE Main 2019 (Online) 8th April Evening Slot
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The sum of the solutions of the equation $$\left| {\sqrt x - 2} \right| + \sqrt x \left( {\sqrt x - 4} \right) + 2 = ...
JEE Main 2019 (Online) 8th April Morning Slot
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The number of integral values of m for which the quadratic expression, (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x $$ \in $$ R...
JEE Main 2019 (Online) 12th January Evening Slot
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If $$\lambda $$ be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m – 4)x + 2 = 0, then the least valu...
JEE Main 2019 (Online) 12th January Morning Slot
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Let $$\alpha $$ and $$\beta $$ be the roots of the quadratic equation x2 sin $$\theta $$ – x(sin $$\theta $$ cos $$\the...
JEE Main 2019 (Online) 11th January Evening Slot
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If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is ...
JEE Main 2019 (Online) 11th January Morning Slot
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The value of $$\lambda $$ such that sum of the squares of the roots of the quadratic equation, x2 + (3 – $$\lambda $$)x ...
JEE Main 2019 (Online) 10th January Evening Slot
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Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c $$ \ne $$ 5. Let S be the set of all integral values of...
JEE Main 2019 (Online) 10th January Morning Slot
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The number of all possible positive integral values of $$\alpha $$ for which the roots of the quadratic equation,...
JEE Main 2019 (Online) 9th January Evening Slot
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If both the roots of the quadratic equation x2 $$-$$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5...
JEE Main 2019 (Online) 9th January Evening Slot
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If an angle A of a $$\Delta $$ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x2 + 27x + 20 =...
JEE Main 2018 (Online) 16th April Morning Slot
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Let p, q and r be real numbers (p $$ \ne $$ q, r $$ \ne $$ 0), such that the roots of the equation $${1 \over {x + p}} ...
JEE Main 2018 (Online) 16th April Morning Slot
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If f(x) is a quadratic expression such that f (1) + f (2) = 0, and $$-$$ 1 is a root of f (x) = 0, then the other root o...
JEE Main 2018 (Online) 15th April Evening Slot
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If tanA and tanB are the roots of the quadratic equation, 3x2 $$-$$ 10x $$-$$ 25 = 0, then the value of 3 sin2(A + B) $$...
JEE Main 2018 (Online) 15th April Morning Slot
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If $$\lambda $$ $$ \in $$ R is such that the sum of the cubes of the roots of the equation, x2 + (2 $$-$$ $$\lambda $$)...
JEE Main 2018 (Online) 15th April Morning Slot
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Let S = { $$x$$ $$ \in $$ R : $$x$$ $$ \ge $$ 0 and $$2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \ri...
JEE Main 2018 (Offline)
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The sum of all the real values of x satisfying the equation 2(x$$-$$1)(x2 + 5x $$-$$ 50) = 1 is : ...
JEE Main 2017 (Online) 9th April Morning Slot
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Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x$$-$$ 1 and it leaves r...
JEE Main 2017 (Online) 8th April Morning Slot
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If for a positive integer n, the quadratic equation $$x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \ri...
JEE Main 2017 (Offline)
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If x is a solution of the equation, $$\sqrt {2x + 1} $$ $$ - \sqrt {2x - 1} = 1,$$ $$\,\,\left( {x \ge {1 \over 2}} \ri...
JEE Main 2016 (Online) 10th April Morning Slot
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If the equations x2 + bx−1 = 0 and x2 + x + b = 0 have a common root different from −1, then $$\left| b \right|$$ is equ...
JEE Main 2016 (Online) 9th April Morning Slot
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The sum of all real values of $$x$$ satisfying the equation $${\left( {{x^2} - 5x + 5} \right)^{{x^2} + 4x - 60}}\, = 1$...
JEE Main 2016 (Offline)
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Let $$\alpha $$ and $$\beta $$ be the roots of equation $${x^2} - 6x - 2 = 0$$. If $${a_n} = {\alpha ^n} - {\beta ^n},$$...
JEE Main 2015 (Offline)
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Let $$\alpha $$ and $$\beta $$ be the roots of equation $$p{x^2} + qx + r = 0,$$ $$p \ne 0.$$ If $$p,\,q,\,r$$ in A.P. a...
JEE Main 2014 (Offline)
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If $$a \in R$$ and the equation $$ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right)...
JEE Main 2014 (Offline)
GO TO QUESTION
If the equations $${x^2} + 2x + 3 = 0$$ and $$a{x^2} + bx + c = 0,$$ $$a,\,b,\,c\, \in \,R,$$ have a common root, then ...
JEE Main 2013 (Offline)
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The number of values of $$k$$, for which the system of equations : $$$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \...
JEE Main 2013 (Offline)
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The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \r...
JEE Main 2013 (Offline)
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The equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has:
AIEEE 2012
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If $$\alpha $$ and $$\beta $$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2...
AIEEE 2010
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If the roots of the equation $$b{x^2} + cx + a = 0$$ imaginary, then for all real values of $$x$$, the expression $$3{b^...
AIEEE 2009
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If $$\,\left| {z - {4 \over z}} \right| = 2,$$ then the maximum value of $$\,\left| z \right|$$ is equal to :
AIEEE 2009
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The quadratic equations $${x^2} - 6x + a = 0$$ and $${x^2} - cx + 6 = 0$$ have one root in common. The other roots of th...
AIEEE 2009
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STATEMENT - 1 : For every natural number $$n \ge 2,$$ $$${1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \o...
AIEEE 2008
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If the difference between the roots of the equation $${x^2} + ax + 1 = 0$$ is less than $$\sqrt 5 ,$$ then the set of po...
AIEEE 2007
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If $$x$$ is real, the maximum value of $${{3{x^2} + 9x + 17} \over {3{x^2} + 9x + 7}}$$ is
AIEEE 2006
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All the values of $$m$$ for which both roots of the equation $${x^2} - 2mx + {m^2} - 1 = 0$$ are greater than $$ - 2$$ b...
AIEEE 2006
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If the roots of the quadratic equation $${x^2} + px + q = 0$$ are $$\tan {30^ \circ }$$ and $$\tan {15^ \circ }$$, respe...
AIEEE 2006
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If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers, then $${b^2} - 4c$$ equals
AIEEE 2005
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The value of $$a$$ for which the sum of the squares of the roots of the equation $${x^2} - \left( {a - 2} \right)x - a -...
AIEEE 2005
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If both the roots of the quadratic equation $${x^2} - 2kx + {k^2} + k - 5 = 0$$ are less than 5, then $$k$$ lies in the...
AIEEE 2005
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In a triangle $$PQR,\;\;\angle R = {\pi \over 2}.\,\,If\,\,\tan \,\left( {{P \over 2}} \right)$$ and $$ \tan \left( {{Q...
AIEEE 2005
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If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $${x^2} + px + q = 0$$ has equal roots, t...
AIEEE 2004
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If $$\left( {1 - p} \right)$$ is a root of quadratic equation $${x^2} + px + \left( {1 - p} \right) = 0$$ then its ro...
AIEEE 2004
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Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
AIEEE 2004
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The real number $$x$$ when added to its inverse gives the minimum value of the sum at $$x$$ equal to
AIEEE 2003
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The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is
AIEEE 2003
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The value of '$$a$$' for which one root of the quadratic equation $$$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a ...
AIEEE 2003
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If the sum of the roots of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the sum of the squares of their re...
AIEEE 2003
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If $$a,\,b,\,c$$ are distinct $$ + ve$$ real numbers and $${a^2} + {b^2} + {c^2} = 1$$ then $$ab + bc + ca$$ is
AIEEE 2002
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If $$p$$ and $$q$$ are the roots of the equation $${x^2} + px + q = 0,$$ then
AIEEE 2002
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Difference between the corresponding roots of $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ is same and $$a \ne b,$...
AIEEE 2002
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Product of real roots of equation $${t^2}{x^2} + \left| x \right| + 9 = 0$$
AIEEE 2002
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If $$\alpha \ne \beta $$ but $${\alpha ^2} = 5\alpha - 3$$ and $${\beta ^2} = 5\beta - 3$$ then the equation having $...
AIEEE 2002
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