Use the Rational Roots Test to Find All Possible Roots n(t)=25t^3-85t^2+67t+17

$n (t) = 25 t^{3} - 85 t^{2} + 67 t + 17$

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.

$p = \pm 1, \pm 17$

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

Step 2

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

$\pm 1, \pm \frac{1}{5}, \pm \frac{1}{25}, \pm 17, \pm \frac{17}{5}, \pm \frac{17}{25}$

Use the Rational Roots Test to Find All Possible Roots n(t)=25t^3-85t^2+67t+17

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