Use the Rational Roots Test to Find All Possible Roots 0=15x^4-x^2+25

$0 = 15 x^{4} - x^{2} + 25$

Step 1

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

Subtract $15 x^{4}$ from both sides of the equation.

$- 15 x^{4} = - x^{2} + 25$

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

$- 15 x^{4} + x^{2} = 25$

Subtract $25$ from both sides of the equation.

$- 15 x^{4} + x^{2} - 25 = 0$

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.

$p = \pm 1, \pm 5, \pm 25$

$q = \pm 1, \pm 3, \pm 5, \pm 15$

Step 3

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

$\pm 1, \pm \frac{1}{3}, \pm \frac{1}{5}, \pm \frac{1}{15}, \pm 5, \pm \frac{5}{3}, \pm 25, \pm \frac{25}{3}$

Use the Rational Roots Test to Find All Possible Roots 0=15x^4-x^2+25

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