It is given that ‒1 is one of the zeros of the polynomial x3 + 2x2 ‒ 11x ‒ 12. Find all the zeros of the given polynomial.
Let us assume f (x) = x3 + 2x2 ‒ 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) = x3 + 2x2 ‒ 11x ‒ 12
= (x + 1) (x2 + x – 12)
= (x + 1) {x2 + 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