Let a, b, c be real numbers, $$a \ne 0$$. If $$\alpha \,$$ is a root of $${a^2}{x^2} + bx + c = 0$$. $$\beta \,$$ is the root of $${a^2}{x^2} - bx - c = 0$$ and $$0 < \alpha \, < \,\beta $$, then the equation $${a^2}{x^2} + 2bx + 2c = 0$$ has a root $$\gamma $$ that always satisfies
A
$$\gamma = {{\alpha + \beta } \over 2}$$
B
$$\gamma = \alpha + {\beta \over 2}$$
C
$$\gamma = \alpha $$
D
$$\alpha < \gamma < \beta $$
3
IIT-JEE 1989
MCQ (More than One Correct Answer)
If $$\alpha $$ and $$\beta $$ are the roots of $${x^2}$$+ px + q = 0 and $${\alpha ^4},{\beta ^4}$$ are the roots of $$\,{x^2} - rx + s = 0$$, then the equation $${x^2} - 4qx + 2{q^2} - r = 0$$ has always
A
two real roots
B
two positive roots
C
two negative roots
D
one positive and one negative root.
4
IIT-JEE 1989
MCQ (More than One Correct Answer)
The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has
A
at least one real solution
B
exactly three solutions
C
exactly one irrational solution
D
complex roots.
Questions Asked from Quadratic Equation and Inequalities
On those following papers in MCQ (Multiple Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
