Question

Find all zeroes of the polynomial $2x^3+x^2-6x-3$ if two of its zeroes are $-\sqrt{3}$ & $\sqrt{3}$

Answer 1

Given polynomial is $2x^3+x^2-6x-3$

The two roots of polynomial are $-\sqrt{3},\sqrt{3}$

Let the other root be $a$

Product of the roots will be $=-\frac{(-d)}{a}=-\frac{(-3)}{2}$

$=(-\sqrt{3})\left(\sqrt{3}\right)a=\frac{3}{2}$

$=a=-\frac{1}{2}$

So the other zero is $-\frac{1}{2}$