It is given that ‒1 is one of the zeros of the polynomial x^{3} + 2x^{2} ‒ 11x ‒ 12. Find all the zeros of the given polynomial.

Let us assume f (x) = x^{3} + 2x^{2} ‒ 11x ‒ 12

It is given in the question that, -1 is a zero of the polynomial

∴ (x + 1) is a factor of f (x)

Now on dividing f (x) by (x + 1), we get

f (x) = x^{3} + 2x^{2} ‒ 11x ‒ 12

= (x + 1) (x^{2} + x – 12)

= (x + 1) {x^{2} + 4x – 3x – 12}

= (x + 1) {x (x + 4) – 3 (x + 4)}

= (x + 1) (x – 3) (x + 4)

∴ f (x) = 0

(x + 1) (x – 3) (x + 4) = 0

(x + 1) = 0 0r (x – 3) = 0 or (x + 4) = 0

x = -1 or x = 3 or x = - 4

Hence, zeros of the polynomial are -1, 3 and -4

12