Question

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

Answer 1

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

Let the third Zero be $\alpha$

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

$\alpha =-3$

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