Solve (m-2)^2geq0

$$( m - 2 ) ^ { 2 } \geq 0$$

Solve for m

$$m\in \mathrm{R}$$

Solution Steps

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.

$$\left(m-2\right)^{2}=0$$

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

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

Do the calculations.

$$m=\frac{4±0}{2}$$

Solutions are the same.

$$m=2$$

Rewrite the inequality by using the obtained solutions.

$$\left(m-2\right)^{2}\geq 0$$

Inequality holds for m\in \mathrm{R}.

$$m\in \mathrm{R}$$