Mathematics - Application of Derivative Question with Solution | TestHub

Let $\alpha ,\beta$ be roots of ${\mathrm{x}}^2-\mathrm{bx}+\mathrm{c}=0$,

Then $\alpha +\beta =\mathrm{b}$

$\Rightarrow$ one of the roots is '2' (Since $\alpha ,\beta$ are primes and b is odd positive integer) $\therefore f(2)=0\Rightarrow 2b-c=4$ and $b+c=35$

$\therefore \mathrm{b}=13,\mathrm{c}=22$

Minimum value $=f\left(\frac{13}{2}\right)=-\frac{81}{4}$.