Mathematics - Quadratic Equation Question with Solution | TestHub

Let roots are $\alpha$ and $3\alpha$, then $4\alpha =4a\Rightarrow \alpha =a$ and

$\begin{array}{rlr}& a^2-4a^2+f(a)=0\Rightarrow f(a)=3a^2-a& \end{array}$

$$f^{\prime }(a)=6a-1,f^{\prime \prime }(a)=6,thenminimumvalueof{f}^{\prime }(a)=6a-1,f^{\prime \prime }(a)=6$$