Use the Rational Roots Test to Find All Possible Roots f(x)=3x^4+5x^3-5x^2+2x-12

$f (x) = 3 x^{4} + 5 x^{3} - 5 x^{2} + 2 x - 12$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$

$q = \pm 1, \pm 3$

Step 2

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

$\pm 1, \pm \frac{1}{3}, \pm 2, \pm \frac{2}{3}, \pm 3, \pm 4, \pm \frac{4}{3}, \pm 6, \pm 12$

Use the Rational Roots Test to Find All Possible Roots f(x)=3x^4+5x^3-5x^2+2x-12

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