Question

Find the zeroes of the polynomial $x^2-3$ and verify the relationship between the zeroes and the coefficients.

Answer 1

Given polynomial is $x^2-3$

Here, $a=1,b=0$ and $c=-3$

$x^2-3=(x-\sqrt{3})(x-\sqrt{3})$

So, the value of $x^2-3$ is zero when $x=\sqrt{3}$ or $x=-\sqrt{3}$

Threrfore , thr zeroes of $x^2-3$ are $\sqrt{3}$ and $-\sqrt{3}$.

Now, sum of zeroes $=\sqrt{3}-\sqrt{3}=0=\frac{0}{1}=\frac{-b}{a}$

product of zeroes $=\left(\sqrt{3}\right)(-\sqrt{3})=-3=\frac{-3}{1}=\frac{c}{a}$

Hence verified.