Use the Rational Roots Test to Find All Possible Roots f(x)=x^4-4x^3-3x^2+16x-4

$f (x) = x^{4} - 4 x^{3} - 3 x^{2} + 16 x - 4$

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.

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

$q = \pm 1$

Step 2

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

$\pm 1, \pm 2, \pm 4$

Use the Rational Roots Test to Find All Possible Roots f(x)=x^4-4x^3-3x^2+16x-4

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