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# Which of the following represents the zeros of f(x) = x^{3} - 3x^{2} - 2x + 6?

-3, -√2, -√2

3, -√2, -√2

-3, √2, √2

3, √2, -√2

**Solution:**

Given function is f(x) = x^{3} - 3x^{2} - 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 x^{2 }- 2

Now take x^{2 }- 2 = 0

⇒ x^{2} = 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) = x^{3} - 3x^{2} - 2x + 6?

**Summary:**

The zeros of f(x) = f(x) = x^{3} - 3x^{2} - 2x + 6 are 3, ±√2.

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