Question

Obtain all zeroes of f(x) = x3 + 13x2 + 32x + 20, if one of its zeros is -2.

Answer 1

Given,

f(x)= x3 + 13x2 + 32x + 20

And, -2 is one of the zeros. So, (x + 2) is a factor of f(x),

Performing division algorithm, we get

⇒ f(x) = (x2 + 11x + 10)( x + 2)

So, putting x2 + 11x + 10 = 0 we can get the other 2 zeros.

⇒ (x + 10)(x + 1) = 0

∴ x = -10 or -1

Hence, all the zeros of the polynomial are -10, -2 and -1.