Question

If the origin lies between zeroes of the polynomial $f\left(x\right)=\frac{x^2}{4}-ax+a^2+a-2$ , then the number of integral value(s) of $a$ is

• A. $1$
• B. $2$
• C. $3$
• D. more than $3$

Answer 1

Answer: (B)

For zeroes on either side of the origin.
Opening upward parabola
$\Rightarrow f\left(0\right)<0$
$\Rightarrow a^2+a-2<0$
$\Rightarrow \left(a+2\right)\left(a-1\right)<0$
$\Rightarrow -2<a<1$
$\Rightarrow 2$ integers i.e. $\left\{-1,0\right\}$