Solve 3y^4-11y^2-4=0

$$3 y ^ { 4 } - 11 y ^ { 2 } - 4 = 0$$

Solve for y (complex solution)

$$y=2$$

$$y=-2$$

$$y=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$y=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$3t^{2}-11t-4=0$$

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, -11 for b, and -4 for c in the quadratic formula.

$$t=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 3\left(-4\right)}}{2\times 3}$$

Do the calculations.

$$t=\frac{11±13}{6}$$

Solve the equation t=\frac{11±13}{6} when ± is plus and when ± is minus.

$$t=4 t=-\frac{1}{3}$$

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

$$y=-2 y=2 y=-\frac{\sqrt{3}i}{3} y=\frac{\sqrt{3}i}{3}$$

Solve for y

$$y=-2$$

$$y=2$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$3t^{2}-11t-4=0$$

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, -11 for b, and -4 for c in the quadratic formula.

$$t=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 3\left(-4\right)}}{2\times 3}$$

Do the calculations.

$$t=\frac{11±13}{6}$$

Solve the equation t=\frac{11±13}{6} when ± is plus and when ± is minus.

$$t=4 t=-\frac{1}{3}$$

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

$$y=2 y=-2$$