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13 days ago

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According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 –

2x4 + 9x3 – x2 + 12?
A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48

2 answers:

lawyer [9.2K]13 days ago

5 0

<span>Based on the Rational Root Theorem, </span><span>f(x) = 3x^5 – 2x^4 – 9x^3 + x^2 – 12 shares the same potential rational roots as the function </span>g(x) = 3x^5 – 2x^4 + 9x^3 – x^2 + 12

lawyer [9.2K]13 days ago

4 0

We need to determine which function shares the identical set of potential rational roots with the function $g(x)= 3x^5-2x^4+9x^3-x^2+12$ .

To begin, we will calculate the rational roots of the provided function.

Let 'p' represent the factors of 12

Thus, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' denote the factors of 3

Accordingly, q= $\pm 1, \pm 3$

Hence, the rational roots are calculated through $\frac{p}{q}$ , which are:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Now, we look at the function presented in part A.

f(x) = $3x^5-2x^4-9x^3+x^2-12$

Again, let 'p' be the factors of 12

Thus, p= $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6$

Let 'q' represent the factors of 3

Resulting in q= $\pm 1, \pm 3$

Thus, the rational roots are derived from $\frac{p}{q}$ , leading to:

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}$ .

Consequently, this equation possesses the same rational roots as the original function.

Thus, option A is the correct choice.

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