Solve 3x^4-17x^2+10=0

$$3 x ^ { 4 } - 17 x ^ { 2 } + 10 = 0$$

Solve for x

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$3t^{2}-17t+10=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 3 for a, -17 for b, and 10 for c in the quadratic formula.

$$t=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 3\times 10}}{2\times 3}$$

Do the calculations.

$$t=\frac{17±13}{6}$$

Solve the equation t=\frac{17±13}{6} when ± is plus and when ± is minus.

$$t=5 t=\frac{2}{3}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=\sqrt{5} x=-\sqrt{5} x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$