Question

Find the zeros of the polynomial $4x^2-9.$

Answer 1

Factorise the polynomial $4x^2-9=0$:

Let the polynomial $p\left(x\right)=4x^2-9$.

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

By using factor theorem, $p\left(a\right)=0$.

$\begin{array}{cc}\Rightarrow & 4a^2-9=0\\ \Rightarrow & 4a^2=9\\ \Rightarrow & a^2=\frac{9}{4}\\ \Rightarrow & a=\pm \frac{3}{2}\end{array}$

Hence, the required zeros of polynomial are $+\frac{3}{2},-\frac{3}{2}$.