Use the Rational Roots Test to Find All Possible Roots 2x^4-9x^3+22x^2-54x+60=0

$2 x^{4} - 9 x^{3} + 22 x^{2} - 54 x + 60 = 0$

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.

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

$q = \pm 1, \pm 2$

Step 2

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

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

Use the Rational Roots Test to Find All Possible Roots 2x^4-9x^3+22x^2-54x+60=0

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