Use the Rational Roots Test to Find All Possible Roots 0=6x^4-x^2+4

$0 = 6 x^{4} - x^{2} + 4$

Step 1

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

Subtract $6 x^{4}$ from both sides of the equation.

$- 6 x^{4} = - x^{2} + 4$

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

$- 6 x^{4} + x^{2} = 4$

Subtract $4$ from both sides of the equation.

$- 6 x^{4} + x^{2} - 4 = 0$

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.

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

$q = \pm 1, \pm 2, \pm 3, \pm 6$

Step 3

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

$\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}, \pm 2, \pm \frac{2}{3}, \pm 4, \pm \frac{4}{3}$

Use the Rational Roots Test to Find All Possible Roots 0=6x^4-x^2+4

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