Use the Rational Roots Test to Find All Possible Roots f(x)=2x^4-5x^3-20x^2+115x-52

$f (x) = 2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52$

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.

$p = \pm 1, \pm 2, \pm 4, \pm 13, \pm 26, \pm 52$

$q = \pm 1, \pm 2$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm 2, \pm 4, \pm 13, \pm \frac{13}{2}, \pm 26, \pm 52$

Use the Rational Roots Test to Find All Possible Roots f(x)=2x^4-5x^3-20x^2+115x-52

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