Solve 4k^2-8k+4>0

$$4 k ^ { 2 } - 8 k + 4 > 0$$

Solve for k

$$k\neq 1$$

Steps Using the Quadratic Formula

To solve the inequality, factor the left hand side. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$4k^{2}-8k+4=0$$

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 4 for a, -8 for b, and 4 for c in the quadratic formula.

$$k=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 4\times 4}}{2\times 4}$$

Do the calculations.

$$k=\frac{8±0}{8}$$

Solutions are the same.

$$k=1$$

Rewrite the inequality by using the obtained solutions.

$$4\left(k-1\right)^{2}>0$$

Inequality holds for k\neq 1.

$$k\neq 1$$