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

In order to know that a number is a root or a zero of the equation is by substituting the roots to x. If the answer is equal to zero, then that's a root.

f(4) = 4^3 - 4(4)^2 - 5(4) + 20
f(4) = 0
Then 4 is a root.

f(-4) = (-4)^3 - 4(-4)^2 - 5(-4) + 20
f(-4) = -88
Then -4 is not a root.

f(sq rt 5) = sq rt 5^3 - 4(sq rt 5)^2 - 5(sq rt 5) + 20
f(sq rt 5) = -4 sq rt 5
Then sq rt of 5 is not a root

f(sq rt -5) = sq rt -5^3 - 4(sq rt -5)^2 - 5(sq rt 5) + 20
f(sq rt -5) = -4 sq rt -5 + 20
Then sq rt of 5 is not a root

Then the only root is 4