Question

The range of $a$ for which the equation $x^2+ax-4=0$ has its smaller root in the interval $(-1,2)$ is

• A. $(-\infty ,-3)$
• B. $(0,3)$
• C. $(0,\infty )$
• D. $(-\infty ,-3)\cup (0,\infty )$

Answer 1

The correct option is A $(-\infty ,-3)$

Clearly, $f(-1)>0,f\left(2\right)<0$
Now, $f\left(0\right)=-4<0$
$\Rightarrow f(-1)=1-a-4>0$
and $f\left(2\right)=4+2a-4<0$
$\Rightarrow a<-3$ and $a<0$
$\Rightarrow a\in (-\infty ,-3)$.