Mathematics - Quadratic Equation Question with Solution | TestHub

The given quadratic equation is $x^2-(a+1)x+a=0$. This equation can be factored as $(x-1)(x-a)=0$. The roots of the equation are $x_1=1$ and $x_2=a$. We are looking for exactly one root to lie in the open interval $(1,3)$. Since $x_1=1$ is not included in the open interval $(1,3)$, the other root $x_2=a$ must be the one that lies in this interval. Therefore, we must have $1<a<3$.