Question

use the rational zero theorem to list all possible rational zeros for the given function.

(f(x) = 7x^4 - x^2 + 5)

a. (pm \frac{1}{7}, pm \frac{1}{5}, pm 1, pm 5, pm 7)
b. (pm \frac{1}{7}, pm \frac{5}{7}, pm 1, pm 5)
c. (pm \frac{1}{7}, pm \frac{5}{7}, pm 1, pm 5, pm 7)
d. (pm \frac{1}{5}, pm \frac{7}{5}, pm 1, pm 7)

Explanation:

Identify the leading coefficient and constant term

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK0
$$

Find all factors of the constant term

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK1
$$

Find all factors of the leading coefficient

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK2
$$

Form all possible rational zeros

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK3
$$

Match with the given options

Using the Rational Root Theorem knowledge point

$$
LATEXBLOCK4
$$

Answer:

• A. \(\pm \frac{1}{7}, \pm \frac{1}{5}, \pm 1, \pm 5, \pm 7\)
• B. \(\pm \frac{1}{7}, \pm \frac{5}{7}, \pm 1, \pm 5\) (Correct answer)
• C. \(\pm \frac{1}{7}, \pm \frac{5}{7}, \pm 1, \pm 5, \pm 7\)
• D. \(\pm \frac{1}{5}, \pm \frac{7}{5}, \pm 1, \pm 7\)