Disequazione di secondo grado $-x^2+4x-3\ge 0$

Text

Solve the inequality $-x^2+4x-3\ge 0.$

Solution

Multiplying by $-1$ (and flipping the sign) gives $x^2-4x+3\le 0$. The roots are $x=1$ and $x=3$. The parabola $y=x^2-4x+3$ is positive outside, hence $\le 0$ between the roots: $\boxed{1\le x\le 3.}$