Which of the following represents the zeros of f(x) = x³ - 3x² - 2x + 6?
-3, -√2, -√2
3, -√2, -√2
-3, √2, √2
3, √2, -√2

Solution:

Given function is f(x) = x³ - 3x² - 2x + 6

From the options given, x = 3 or x = -3 is a solution for the given function. We have to find the roots of the equation. Let us check by inspection.

f(3) = (3)³ - 3(3)² - 2(3) + 6 = 0

x = 3 is a root.

To find remaining roots let us use the synthetic division method.

Quotient is x² - 2

Now take x² - 2 = 0

⇒ x² = 2

⇒ x = ±√2

Therefore, the roots/zeros of the given function are 3, ±√2.

Option (iv) is the answer.

Which of the following represents the zeros of f(x) = x³ - 3x² - 2x + 6?

Summary:

The zeros of f(x) = f(x) = x³ - 3x² - 2x + 6 are 3, ±√2.