Q. One lies between the roots of the equation $–x^{2} + ax + a = 0,\ a \in R$ if and only if $a$ lies in the interval
A) $\left( \frac{1}{2},\ \infty \right)$
B) $\left\lbrack \ - \frac{1}{2},\ \infty \right)$
C) $\left( \ - \ \infty,\frac{1}{2} \right)$
D) $\left( \ - \ \infty,\frac{1}{2} \right\rbrack$
Explanation
(a)
$–x^{2} + ax + a = 0$
$\Rightarrow {\ x}^{2} - ax - a = 0$
Let $f(x) = x^{2} - ax - a$
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$f(1) < 0$
$\Rightarrow 1 - a - a < 0$
$\Rightarrow 1 < 2a$
$\Rightarrow a > \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.