Use the Rational Roots Test to Find All Possible Roots f(x)=35x^4-x^2+49

$f (x) = 35 x^{4} - x^{2} + 49$

Step 1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 7, \pm 49$

$q = \pm 1, \pm 5, \pm 7, \pm 35$

Step 2

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm \frac{1}{5}, \pm \frac{1}{7}, \pm \frac{1}{35}, \pm 7, \pm \frac{7}{5}, \pm 49, \pm \frac{49}{5}$

Use the Rational Roots Test to Find All Possible Roots f(x)=35x^4-x^2+49

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