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

Solution:

Given: Function f(x) = x³ - 4x² - 5x + 20

Since we know “4” is one of the values, we can solve using f(4) and see whether it is zero.

⇒ f(4) = (4)³ - 4(4)² - 5(4) + 20

⇒ f(4) = 64 - 64 - 20 + 20

⇒f(4) = 0

Therefore, (x - 4) is a factor.

By long division,

The given equation x³ - 4x² - 5x + 20 = 0 becomes

⇒(x - 4)(x² - 5) = 0

We already know 4 is a root of the given equation.

⇒ (x² - 5) = 0

⇒ x² = 5

Taking square root,

⇒ √x² = √5

⇒ x = ±√5

Therefore, the zeros of the function are x = 4 and x = ±√5.

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

Summary:

4, square root of 5, -square root of 5 represents the zeros of f(x) = x³ - 4x² - 5x + 20.