Use the Rational Roots Test to Find All Possible Roots 0=33x^4-x^2+9

$0 = 33 x^{4} - x^{2} + 9$

Step 1

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

Subtract $33 x^{4}$ from both sides of the equation.

$- 33 x^{4} = - x^{2} + 9$

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

$- 33 x^{4} + x^{2} = 9$

Subtract $9$ from both sides of the equation.

$- 33 x^{4} + x^{2} - 9 = 0$

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.

$p = \pm 1, \pm 3, \pm 9$

$q = \pm 1, \pm 3, \pm 11, \pm 33$

Step 3

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

$\pm 1, \pm \frac{1}{3}, \pm \frac{1}{11}, \pm \frac{1}{33}, \pm 3, \pm \frac{3}{11}, \pm 9, \pm \frac{9}{11}$

Use the Rational Roots Test to Find All Possible Roots 0=33x^4-x^2+9

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