Use the Rational Roots Test to Find All Possible Roots 0=21x^4-x^2+49

$0 = 21 x^{4} - x^{2} + 49$

Step 1

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

Subtract $21 x^{4}$ from both sides of the equation.

$- 21 x^{4} = - x^{2} + 49$

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

$- 21 x^{4} + x^{2} = 49$

Subtract $49$ from both sides of the equation.

$- 21 x^{4} + x^{2} - 49 = 0$

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.

$p = \pm 1, \pm 7, \pm 49$

$q = \pm 1, \pm 3, \pm 7, \pm 21$

Step 3

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

$\pm 1, \pm \frac{1}{3}, \pm \frac{1}{7}, \pm \frac{1}{21}, \pm 7, \pm \frac{7}{3}, \pm 49, \pm \frac{49}{3}$

Use the Rational Roots Test to Find All Possible Roots 0=21x^4-x^2+49

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