Question

Which of the following represents the zeros of f(x) = x3 − 4x2 − 5x + 20?

−4, −square root of 5 , −square root of 5

4, square root of 5 , −square root of 5

4, −square root of 5 , −square root of 5

−4, square root of 5 , square root of 5

Answer 1

The zeroes of f(x) are 4 , √5 , -√5

Explanation:

(x - 4) is a factor of f(x) because : (x = 4)

(4)³ - 4(4)² - 5(4) + 20 = 0

(x - √5) is a factor of f(x) because : (x = √5)

(√5)³ - 4(√5)² -5(√5) + 20 = 0

(x + √5) is a factor of f(x) because : (x = -√5)

(-√5)³ - 4(-√5)² -5(-√5) + 20 = 0

∴ The zeroes of f(x) are 4 , √5 , -√5