Solve k^4-7k^2+10=0

$$k ^ { 4 } - 7 k ^ { 2 } + 10 = 0$$

Solve for k

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

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

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

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

Steps Using the Quadratic Formula

Substitute t for k^{2}.

$$t^{2}-7t+10=0$$

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 1 for a, -7 for b, and 10 for c in the quadratic formula.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\times 10}}{2}$$

Do the calculations.

$$t=\frac{7±3}{2}$$

Solve the equation t=\frac{7±3}{2} when ± is plus and when ± is minus.

$$t=5 t=2$$

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

$$k=\sqrt{5} k=-\sqrt{5} k=\sqrt{2} k=-\sqrt{2}$$