Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = 7 x ^ { 4 } - x ^ { 2 } + 3$$
A) $\pm \frac { 1 } { 3 } , \pm \frac { 7 } { 3 } , \pm 1 , \pm 7$
B) $\pm \frac { 1 } { 7 } , \pm \frac { 3 } { 7 } , \pm 1 , \pm 3$
C) $\pm \frac { 1 } { 7 } , \pm \frac { 3 } { 7 } , \pm 1 , \pm 3 , \pm 7$
D) $\pm \frac { 1 } { 7 } , \pm \frac { 1 } { 3 } , \pm 1 , \pm 3 , \pm 7$

Question

Quizplus · Accepted Answer

The Rational Zeros Theorem states that any rational zero of a polynomial function $f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$, where all coefficients are integers, can be expressed in the form $\pm \frac{p}{q}$, where $p$ is a factor of the constant term $a_0$ and $q$ is a factor of the leading coefficient $a_n$. For the given polynomial $f(x) = 7x^4 - x^2 + 3$, the constant term $a_0 = 3$ and the leading coefficient $a_n = 7$. The factors of 3 are $\pm 1, \pm 3$, and the factors of 7 are $\pm 1, \pm 7$. Therefore, the potential rational zeros are $\pm \frac{1}{7}, \pm \frac{3}{7}, \pm 1, \pm 3$.

Use the Rational Zeros Theorem to Determine the Potential Rational f(x)=7x4−x2+3f ( x ) = 7 x ^ { 4 } - x ^ { 2 } + 3f(x)=7x4−x2+3

Use the Rational Zeros Theorem to Determine the Potential Rational $f ( x ) = 7 x ^ { 4 } - x ^ { 2 } + 3$