Use the Rational Roots Test to Find All Possible Roots f(x)=-4x^3+23x^2-14x-5

$f (x) = - 4 x^{3} + 23 x^{2} - 14 x - 5$

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.

$p = \pm 1, \pm 5$

$q = \pm 1, \pm 2, \pm 4$

Step 2

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{4}, \pm 5, \pm \frac{5}{2}, \pm \frac{5}{4}$

Use the Rational Roots Test to Find All Possible Roots f(x)=-4x^3+23x^2-14x-5

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