Question

Let $P(x)=x^2+ax+1$. If $P(x)$ is a negative integer for only one real $x$, then product of all values of ' $a$ ' is $

• A. -2$
• B. -4
• C. -6
• D. -8

Answer 1

Answer: (D)

$P(x)={\left(x+\frac{a}{2}\right)}^2+1-\frac{a^2}{4}$
$\therefore 1-\frac{a^2}{4}=-1$
$\Rightarrow a^2=8\Rightarrow a=\pm \sqrt{8}$
$\therefore$ Product is -8 .