1

IIT-JEE 1995

Subjective
Let $$a,\,b,\,c$$ be real. If $$a{x^2} + bx + c = 0$$ has two real roots $$\alpha $$ and $$\beta ,$$ where $$\alpha < - 1$$ and $$\beta > 1,$$ then show that $$1 + {c \over a} + \left| {{b \over a}} \right| < 0.$$

Answer

Solve it.
2

IIT-JEE 1988

Subjective
Solve $$\left| {{x^2} + 4x + 3} \right| + 2x + 5 = 0$$

Answer

$$ - 4,\,\left( { - 1\, - \sqrt 3 } \right)$$
3

IIT-JEE 1987

Subjective
Find the set of all $$x$$ for which $${{2x} \over {\left( {2{x^2} + 5x + 2} \right)}}\, > \,{1 \over {\left( {x + 1} \right)}}$$

Answer

$$\left( { - 2,\, - 1} \right) \cup \left( {{{ - 2} \over 3},\,{{ - 1} \over 2}} \right)$$
4

IIT-JEE 1986

Subjective
For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$

Answer

$$\left\{ {a \pm a\sqrt 2 ,\,\, - a \pm a\sqrt 6 } \right\}$$

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