Question

If the roots of the equation $x^{2}+x+a=0$ exceed $a$, then

• A. a > 2
• B. a < - 2
• C. 2 < a < 3
• D. - 2 < a < - 1

Answer 1

Answer: (B)

For the quadratic equation $x^{2}+x+a=0$, if roots exceed ' $a^{\prime}$, then
$a^{2}+a+a>0$
$\Rightarrow a \in(-\infty,-2) \cup(0, \infty)\,....(i)$
and $D=1-4 a \geq 0$
$\Rightarrow a \in\left(-\infty, \frac{1}{4}\right)\,...(ii)$
and $-\frac{1}{2}>a$
$\Rightarrow a<-\frac{1}{2}$
$\Rightarrow a \in\left(-\infty,-\frac{1}{2}\right)\,,....(iii)$
From Eqs. (i), (ii) and (iii),
$a < − 2$