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

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

Solve for x

$$x = -\frac{9 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{78} + 9} + \sqrt[3]{9 - \sqrt{78}})}}{9} \approx -1.521379707$$

$$x=0$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

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

Do the calculations.

$$t=\frac{1±\sqrt{-7}}{2}$$

Since the square root of a negative number is not defined in the real field, there are no solutions.

$$t\in \emptyset$$

Since t=x^{2}, the original equation does not have any solutions.

$$x\in \emptyset$$