Use the Rational Roots Test to Find All Possible Roots f(x)=7x^4-6x^3+174x^2-150x-25

$f (x) = 7 x^{4} - 6 x^{3} + 174 x^{2} - 150 x - 25$

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.

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

$q = \pm 1, \pm 7$

Step 2

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

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

Use the Rational Roots Test to Find All Possible Roots f(x)=7x^4-6x^3+174x^2-150x-25

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