Question

Obtain all zeros of the polynomial f(x) = x⁴ - 3x³ - x² + 9x - 6 if two of its zeros are -√3 and √3.

Answer 1

We know that if x = a is a zero of a polynomial then

x - a is a factor pf f(x).

Since -√3 and √3 are zeros of f(x).

Therefore (x + √3) and (x - √3) are factors of f(x).

Now on dividing f(x) = x⁴ - 3x³ - x² + 9x - 6 by g(x) = (x - √3)(x + √3) = x² - 3 to find other zeros.

By applying division algorithm, we have:

Hence, the zeros of the given polynomial are:

-√3, √3, 1, 2