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

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

Solve for x

$$x=-\sqrt{3}\approx -1.732050808$$

$$x=\sqrt{3}\approx 1.732050808$$

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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, -10 for b, and 3 for c in the quadratic formula.

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

Do the calculations.

$$t=\frac{10±8}{6}$$

Solve the equation t=\frac{10±8}{6} when ± is plus and when ± is minus.

$$t=3 t=\frac{1}{3}$$

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

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