# Which of the following represents the zeros of f(x) = 6x^{3} - 35x^{2} + 26x - 5?

-5,1/3,1/2

5,-1/3,1/2

5,1/3,-1/2

5,1/2,1/3

**Solution:**

Given, f(x) = 6x^{3} - 35x^{2} + 26x - 5

From the options above, we know “5” is one of the factors of the function f(x) = 6x^{3} - 35x^{2} + 26x - 5.

When x = 5

f(5) = 6(5)^{3} - 35(5)^{2} + 26(5) - 5

f(5) = 750 - 875 + 130 - 5

f(5) = 0

Thus, (x - 5) is a factor of f(x) = 6x^{3} - 35x^{2} + 26x - 5

When x = 1/2

f(1/2) = 6(1/2)^{3} - 35(1/2)^{2} + 26(1/2) - 5

f(1/2) = 3/4 - 35/4 + 13 - 5

f(1/2) = 0.75 - 8.75 + 13 - 5

f(1/2) = 0

Thus, (x - 1/2) is a factor of f(x) = 6x^{3} - 35x^{2} + 26x - 5

When x = 1/3

f(1/3) = 6(1/3)^{3} - 35(1/3)^{2} + 26(1/3) - 5

f(1/3) = 2/9 - 35/9 + 26/3 - 5

f(1/3) = 0

Thus, (x - 1/3) is a factor of f(x) = 6x^{3} - 35x^{2} + 26x - 5

When x = -1/2

f(1/2) = 6(-1/2)^{3} - 35(-1/2)^{2} + 26(-1/2) - 5

f(1/2) = -3/4 - 35/4 - 13 - 5

f(1/2) = -0.75 - 8.75 - 13 - 5 = -27.5

f(1/2) ≠ 0

Thus, (x + 1/2) is not a factor of f(x) = 6x^{3} - 35x^{2} + 26x - 5

When x = -1/3

f(1/3) = 6(-1/3)^{3} - 35(-1/3)^{2} + 26(-1/3) - 5

f(1/3) = -2/9 - 35/9 - 26/3 - 5 = -17.79

f(1/3) ≠ 0

Thus, (x + 1/3) is a factor of f(x) = 6x^{3} - 35x^{2} + 26x - 5

Therefore, the factors of f(x) = 6x^{3} - 35x^{2} + 26x - 5 are 5, 1/2 and 1/3.

## Which of the following represents the zeros of f(x) = 6x^{3} - 35x^{2} + 26x - 5?

**Summary:**

The zeros of f(x) = 6x^{3} - 35x^{2} + 26x - 5 are 5, 1/2 and 1/3. Hence last option is the correct answer.

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