Solve n^4-3n^2+2=0

$$n ^ { 4 } - 3 n ^ { 2 } + 2 = 0$$

Solve for n

$$n=-\sqrt{2}\approx -1.414213562$$

$$n=\sqrt{2}\approx 1.414213562$$

$$n=1$$

$$n=-1$$

Steps Using the Quadratic Formula

Substitute t for n^{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.

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

Do the calculations.

$$t=\frac{3±1}{2}$$

Solve the equation t=\frac{3±1}{2} when ± is plus and when ± is minus.

$$t=2 t=1$$

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

$$n=\sqrt{2} n=-\sqrt{2} n=1 n=-1$$