# Which of the number(s) below are potential roots of the function?q(x) = 6x^{3} + 19x^{2} – 15x – 28

± 2/3, ± 7/2, ± 1/7, ± 6, ± 14, ± 3/5

**Solution:**

q(x) = 6x^{3} + 19x^{2} – 15x – 28 [Given]

Potential roots = factors of the constant term/ factors of the leading coefficient of the function

The factors of constant 28 are 1, 2, 7, 14, and 28.

The factors of coefficient of highest degree 6 are 1, 2, 3, and 6.

The factors can be positive and negative.

By dividing factors of 28 by the factors of 6 provides the potential roots.

Potential roots = factors of 28/ factors of 6

± 1, ± 2, ± 4, ± 7, ± 14, ± 28, ± ½, ± 7/2, ± ⅓, ± ⅔, ± 4/3, ± 7/3, ± 14/3, ± 28/3, ± ⅙, ± 7/6

Therefore, the potential roots of the function among the given options are ± ⅔, ± 7/2, and ±14.

## Which of the number(s) below are potential roots of the function?q(x) = 6x^{3} + 19x^{2} – 15x – 28

± 2/3, ± 7/2, ± 1/7, ± 6, ± 14, ± 3/5

**Summary:**

The number(s) which are potential roots of the function q(x) = 6x^{3} + 19x^{2} – 15x – 28 are ± ⅔, ± 7/2 and ±14.

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