Which of the number(s) below are potential roots of the function?q(x) = 6x3 + 19x2 – 15x – 28
± 2/3, ± 7/2, ± 1/7, ± 6, ± 14, ± 3/5
Solution:
q(x) = 6x3 + 19x2 – 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) = 6x3 + 19x2 – 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) = 6x3 + 19x2 – 15x – 28 are ± ⅔, ± 7/2 and ±14.
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