Question

Find all the zeros of the polynomial $2x^3+x^2-6x-3,$ if two of its zeros are $-\sqrt{3}$ and $\sqrt{3}$.

Answer 1

$f\left(x\right)=2x^3+x^2-6x-3$

Let Third zero be $\alpha$

$\alpha +\sqrt{3}+(-\sqrt{3})=-\frac{1}{2}$

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

So all the zeros of $f\left(x\right)$ are $-\sqrt{3},\sqrt{3},-\frac{1}{2}$