Solve 2x^4-3x^2+11x=0

$$2 x ^ { 4 } - 3 x ^ { 2 } + 11 x = 0$$

Solve for x

$$x = -\frac{4 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{119} + 11} + \sqrt[3]{11 - \sqrt{119}})}}{4} \approx -2.046380326$$

$$x=0$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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 2 for a, -3 for b, and 11 for c in the quadratic formula.

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

Do the calculations.

$$t=\frac{3±\sqrt{-79}}{4}$$

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.

$$x\in \emptyset$$