Question

If √5 and – √5 are two zeroes of the polynomial x³ + 3x² – 5x – 15, then its third zero is
A. 3
B. – 3
C. 5
D. – 5

Answer 1

Answer:

Step-by-step explanation:

Answer is -5

Answer 2

B. – 3

Step-by-step explanation:

Given: Two zeroes of the polynomial x³ + 3x² – 5x – 15 are √5 and – √5.

Find: Third zero.

f(x) = x³ + 3x² – 5x – 15

The two roots of f(x) will be (x+√5) and (x-√5)

So (x+√5)(x-√5) = x² – 5 will be a factor of f(x).

Let divide f(x) by x² – 5:

x³ + 3x² – 5x – 15 / x² – 5 = x + 3

So the third factor of f(x) is  (x + 3).

Third zero will be -3.

Option B is the answer.