Question

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

A
2<a<3
B
a>3
C
3<a<3
D
a<2

Solution

## The correct option is D $$a<-2$$For both roots to exist,$$D>0$$$$\Rightarrow 1-4a>0$$$$a<\dfrac{1}{4}$$$$\Rightarrow a\in (-\infty ,\dfrac{1}{4})$$For both roots to exceed $$a$$, $$f(a)>0$$$$\Rightarrow a^{2}+2a>0$$$$a(a+2)>0$$$$a\in (-\infty ,-2)\bigcup (0,-\infty )$$$$\therefore a\in (-\infty ,-2)$$ for roots to exists and exceed $$a$$.$$\Rightarrow a<-2$$Maths

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