Use the Rational Roots Test to Find All Possible Roots 0=55x^4-x^2+121

$0 = 55 x^{4} - x^{2} + 121$

Step 1

Move all the expressions to the left side of the equation.

Subtract $55 x^{4}$ from both sides of the equation.

$- 55 x^{4} = - x^{2} + 121$

Add $x^{2}$ to both sides of the equation.

$- 55 x^{4} + x^{2} = 121$

Subtract $121$ from both sides of the equation.

$- 55 x^{4} + x^{2} - 121 = 0$

Step 2

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.

$p = \pm 1, \pm 11, \pm 121$

$q = \pm 1, \pm 5, \pm 11, \pm 55$

Step 3

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

$\pm 1, \pm \frac{1}{5}, \pm \frac{1}{11}, \pm \frac{1}{55}, \pm 11, \pm \frac{11}{5}, \pm 121, \pm \frac{121}{5}$

Use the Rational Roots Test to Find All Possible Roots 0=55x^4-x^2+121

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