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.