Question

The polynomial $(x^2+a)$ cannot be factorized if $a>0$. Is this statement true or false?

• 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 since a > 0 –a will be 0 for any a,

but square of any number cannot be negative. So there will be no α such that ${\alpha }^2$ is negative.

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