1
IIT-JEE 1995
Subjective
+5
-0
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 $$1 + {c \over a} + \left| {{b \over a}} \right| < 0.$$
2
IIT-JEE 1988
Subjective
+5
-0
Solve $$\left| {{x^2} + 4x + 3} \right| + 2x + 5 = 0$$
3
IIT-JEE 1987
Subjective
+3
-0
Find the set of all $$x$$ for which $${{2x} \over {\left( {2{x^2} + 5x + 2} \right)}}\, > \,{1 \over {\left( {x + 1} \right)}}$$
4
IIT-JEE 1986
Subjective
+5
-0
For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$
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