Question

Find all the zeros of the polynomial x³ + 3x² - 2x - 6, if two of its zeros are -√2 and √2.

Answer 1

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

x - a is a factor of f(x)

Since - √2 and √2 are zeros of f(x)

Therefore (x + √2) and (x - √2) are factors of f(x)

Now on dividing f(x) = x³ + 3x² - 2x - 6 by g(x) = (x - √2)(x + √2) = x² - 2 to find other zeros.

By applying division algorithm, we have:

Hence, the zeros of the given polynomial are:

-√2, √2, -3