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. $\left\{- 1,0\right\}$