Use the Rational Roots Test to Find All Possible Roots 25x^7-x^6-5x^4+x-49

$25 x^{7} - x^{6} - 5 x^{4} + x - 49$

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.

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

$q = \pm 1, \pm 5, \pm 25$

Step 2

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

$\pm 1, \pm \frac{1}{5}, \pm \frac{1}{25}, \pm 7, \pm \frac{7}{5}, \pm \frac{7}{25}, \pm 49, \pm \frac{49}{5}, \pm \frac{49}{25}$

Use the Rational Roots Test to Find All Possible Roots 25x^7-x^6-5x^4+x-49

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