Mathematics - Quadratic Equation Question with Solution | TestHub

The equation $|x^2-5x+6|=1$ implies two cases: $x^2-5x+6=1$ or $x^2-5x+6=-1$. Case 1: $x^2-5x+5=0$. The discriminant is $D=(-5{)}^2-4(1)(5)=25-20=5$. Since $D>0$, this equation has two distinct real roots. Case 2: $x^2-5x+7=0$. The discriminant is $D=(-5{)}^2-4(1)(7)=25-28=-3$. Since $D<0$, this equation has no real roots. Therefore, the original equation has a total of 2 real roots.