Question

Obtain all zeros of the polynomial f(x) = 2x⁴ + x³ - 14x² - 19x - 6, if two of its zeros are -2 and -1.

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 -1 are zeros of f(x)

Therefore

(x + 2)(x + 1) = x² + 3x + 2 is a factor of f(x).

Now on dividing

f(x) = 2x⁴ + x³ - 14x² - 19x - 6 by g(x) = x² + 3x + 2 dividing to find other zeros.

By applying division algorithm, we have:

Hence, the zeros of the given polynomial are:

- \(\frac{1}{2}\),3, - 2, - 1