Which of the following represents the zeros of f(x) = 6x³ - 31x² + 4x + 5?
-5, one third , one half
5, -one third , one half
5, one third , -one half
5, one third , one half

Solution:

Given, f(x) = 6x³ - 31x² + 4x + 5

We have to find the zeros of the quadratic function.

By rational root test,

The factors of the leading coefficient are 1, 2, 3, 6

The factors of the trailing constant are 1, 5

So, (x - 5) is a factor.

By long division,

The factor of 6x² - x - 1 = 6x² - 3x + 2x - 1

= 3x(2x - 1) + 1(2x - 1)

= (3x + 1)(2x -1)

So, x - 5 = 0

⇒ x = 5

3x + 1 = 0

3x = -1

⇒ x = -1/3

2x - 1 = 0

2x = 1

⇒ x = 1/2

Therefore, 5, -1/3 and 1/2 are the zeros of the function.

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Which of the following represents the zeros of f(x) = 6x³ - 31x² + 4x + 5?

Summary:

5, -1/3 and 1/2 represents the zeros of f(x) = 6x³ - 31x² + 4x + 5.