Use the Rational Roots Test to Find All Possible Roots f(x)=60x^2-57x-18

$f (x) = 60 x^{2} - 57 x - 18$

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.

$p = \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18$

$q = \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30, \pm 60$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{4}, \pm \frac{1}{5}, \pm \frac{1}{6}, \pm \frac{1}{10}, \pm \frac{1}{12}, \pm \frac{1}{15}, \pm \frac{1}{20}, \pm \frac{1}{30}, \pm \frac{1}{60}, \pm 2, \pm \frac{2}{3}, \pm \frac{2}{5}, \pm \frac{2}{15}, \pm 3, \pm \frac{3}{2}, \pm \frac{3}{4}, \pm \frac{3}{5}, \pm \frac{3}{10}, \pm \frac{3}{20}, \pm 6, \pm \frac{6}{5}, \pm 9, \pm \frac{9}{2}, \pm \frac{9}{4}, \pm \frac{9}{5}, \pm \frac{9}{10}, \pm \frac{9}{20}, \pm 18, \pm \frac{18}{5}$

Use the Rational Roots Test to Find All Possible Roots f(x)=60x^2-57x-18

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