Use the Rational Roots Test to Find All Possible Roots f(x)=3x^4-2x^3+74x^2-50x-25

$f (x) = 3 x^{4} - 2 x^{3} + 74 x^{2} - 50 x - 25$

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.

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

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 5, \pm \frac{5}{3}, \pm 25, \pm \frac{25}{3}$

Use the Rational Roots Test to Find All Possible Roots f(x)=3x^4-2x^3+74x^2-50x-25

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