Question

If two zeroes of the polynomial x³ + x² – 9x – 9 are 3 and – 3, then its third zero is
A. – 1
B. 1
C. – 9
D. 9

Answer 1

A. – 1

Step-by-step explanation:

Given: Two zeroes of the polynomial x³ + x² – 9x – 9 are 3 and – 3.

Find: Third zero.

f(x) = x³ + x² – 9x – 9  

The two roots of f(x) will be (x+3) and (x-3)

So (x+3)(x-3) = x² – 9 will be a factor of f(x).

Let divide f(x) by x² – 9:

x³ + x² – 9x – 9 / x² – 9 = x + 1

x³      – 9x

    x²       -9

    x²       -9

So the third factor of f(x) is  (x + 1).

Third zero will be -1.

Option A is the answer.