Question

Find all the zeros of the polynomial x³ + 3x² − 2x − 6, if two of its zeros are $-\sqrt{2}\mathrm{and}\sqrt{2}$.

Answer 1

We know that if is a zero of a polynomial, and then is a factor of .

Since and are zeros of .

Therefore

is a factor of .Now, we divide by to find the other zeros of .

By using division algorithm we have

Hence, the zeros of the given polynomials are .