Solve a^4-3a^2-2a=0

$$a ^ { 4 } - 3 a ^ { 2 } - 2 a = 0$$

Solve for a

$$a=2$$

$$a=0$$

$$a=-1$$

Steps Using the Quadratic Formula

Substitute t for a^{2}.

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

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 1 for a, -3 for b, and -2 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 1\left(-2\right)}}{2}$$

Do the calculations.

$$t=\frac{3±\sqrt{17}}{2}$$

Solve the equation t=\frac{3±\sqrt{17}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{17}+3}{2} t=\frac{3-\sqrt{17}}{2}$$

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

$$a=\frac{\sqrt{2\sqrt{17}+6}}{2} a=-\frac{\sqrt{2\sqrt{17}+6}}{2}$$