1. Tardigrade
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  3. Mathematics
  4. 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

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Q. 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 $

Complex Numbers and Quadratic Equations

Solution:

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