Mathematics - Quadratic Equation Question with Solution | TestHub

Let $\alpha$ be the common root. Then ${\alpha }^2+a\alpha +b=0$ and ${\alpha }^2+b\alpha +a=0$. Subtracting the two equations, we get $(a-b)\alpha +(b-a)=0$, which implies $(a-b)(\alpha -1)=0$. Since $a\ne b$, we must have $\alpha =1$. Substituting $\alpha =1$ into the first equation gives $1+a+b=0$, so $a+b=-1$.