IIT-JEE 2007 | Quadratic Equation and Inequalities Question 23 | Mathematics

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

Let $$\alpha ,\,\beta $$ be the roots of the equation $${x^2} - px + r = 0$$ and $${\alpha \over 2},\,2\beta $$ be the roots of the equation $${x^2} - qx + r = 0$$. Then the value of $$r$$

$${2 \over 9}\left( {p - q} \right)\left( {2q - p} \right)$$

$${2 \over 9}\left( {q - p} \right)\left( {2p - q} \right)$$

$${2 \over 9}\left( {q - 2p} \right)\left( {2q - p} \right)$$

$${2 \over 9}\left( {2p - q} \right)\left( {2q - p} \right)$$

IIT-JEE 2006

MCQ (Single Correct Answer)

-0.75

Let $$a,\,b,\,c$$ be the sides of triangle where $$a \ne b \ne c$$ and $$\lambda \in R$$.
If the roots of the equation $${x^2} + 2\left( {a + b + c} \right)x + 3\lambda \left( {ab + bc + ca} \right) = 0$$ are real, then

$$\lambda < {4 \over 3}$$

$$\lambda > {5 \over 3}$$

$$\lambda \in \left( {{1 \over 3},\,{5 \over 3}} \right)$$

$$\lambda \in \left( {{4 \over 3},\,{5 \over 3}} \right)$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

For all $$'x',{x^2} + 2ax + 10 - 3a > 0,$$ then the interval in which '$$a$$' lies is

$$a < - 5$$

$$ - 5 < a < 2$$

$$a > 5$$

$$2 < a < 5$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If one root is square of the other root of the equation $${x^2} + px + q = 0$$, then the realation between $$p$$ and $$q$$ is

$${p^3} - q\left( {3p - 1} \right) + {q^2} = 0$$

$${p^3} - q\left( {3p + 1} \right) + {q^2} = 0$$

$${p^3} + q\left( {3p - 1} \right) + {q^2} = 0$$

$${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$$

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