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 $D=1-4a\ge 0$
$\Rightarrow a\in \left(-\infty ,\frac{1}{4}\right)...(ii)$
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),
$a<-2$