Find all rational zeros of the polynomial function.
-$$f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10$$
A) $5 , - 2 , \frac { 1 } { 4 }$
B) $5 , - 2,1$
C) $- 5,2 , - \frac { 1 } { 4 }$
D) $- 5,2 , - 1$

Question

Quizplus · Accepted Answer

To find the rational zeros of the polynomial $f(x) = 4x^3 + 13x^2 - 37x - 10$, we can use the Rational Root Theorem. This theorem suggests that any rational root, expressed as a fraction $\frac{p}{q}$, must have $p$ as a factor of the constant term (-10) and $q$ as a factor of the leading coefficient (4). The factors of -10 are $\pm1, \pm2, \pm5, \pm10$, and the factors of 4 are $\pm1, \pm2, \pm4$. By testing these possible rational roots, we find that $-5$, $2$, and $-\frac{1}{4}$ are indeed roots of the polynomial, making option C correct.

Find All Rational Zeros of the Polynomial Function f(x)=4x3+13x2−37x−10f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10f(x)=4x3+13x2−37x−10

Find All Rational Zeros of the Polynomial Function $f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10$