Solve (1-a)^2geq0

$$( 1 - a ) ^ { 2 } \geq 0$$

Solve for a

$$a\in \mathrm{R}$$

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.

$$\left(1-a\right)^{2}=0$$

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

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

Do the calculations.

$$a=\frac{2±0}{2}$$

Solutions are the same.

$$a=1$$

Rewrite the inequality by using the obtained solutions.

$$\left(a-1\right)^{2}\geq 0$$

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

$$a\in \mathrm{R}$$