Question

Find the zeroes of polynomial $2x^2-25.$

Answer 1

Factorise the polynomial $2x^2-25=0$:

Let the polynomial $p\left(x\right)=2x^2-25$.

We know that, any real number $\text{'}a\text{'}$ is root or zero of polynomial $p\left(x\right)$ if and only if $p\left(a\right)=0$.

Here, $p\left(a\right)=0$

$\begin{array}{cc}\Rightarrow & 2a^2-25=0\\ \Rightarrow & 2a^2=25\\ \Rightarrow & a^2=\frac{25}{2}\\ \Rightarrow & a=\pm \frac{5}{\sqrt{2}}\end{array}$

Hence, the required zeros of polynomial are $+\frac{5}{\sqrt{2}},-\frac{5}{\sqrt{2}}.$.