Question

The polynomial $(x^2+a)$ cannot be factorized if $a>0$.

• A. True
• B. False

Answer 1

The correct option is A

True

Suppose α be the zero of the polynomial. then ${\alpha }^2+a$ will be equal to zero

${\alpha }^2+a=0$

${\alpha }^2=-a$

but the square of any number cannot be negative.

So there will be no $\alpha$ such that ${\alpha }^2$ is negative.

$(x^2+a)$ cannot be factorized if $a>0$. So the given statement is true.