Mathematics - Application of Derivative Question with Solution | TestHub

If $a$ and $-1$ are the roots of the polynomial, then we get $$\begin{array}{rl}& f(x)=x^2+(1-a)x-a.\\ \therefore & f(1)=2-2a\\ \text{ and }& f(2)=6-3a\\ \text{ As, }& f(1)+f(2)=0\\ \Rightarrow & 2-2a+6-3a=0\Rightarrow a=\frac{8}{5}\end{array}$$ Therefore, the other root is $\frac{8}{5}$