Mathematics - Quadratic Equation Question with Solution | TestHub

Let$f\left(x\right)=a{x}^2+bx+c$be a quadratic equation with roots$\alpha , \beta$

$f\left(2\right)+f\left(-1\right)=0\Rightarrow 5a+b+2c=0$

 Also $f\left(3\right)=0\Rightarrow 9a+3b+c=0$

$\Rightarrow \frac{a}{-5}=\frac{b}{13}=\frac{c}{6}$

Product of roots $\alpha \beta =\frac{c}{a}=-\frac{6}{5}$

We know $\alpha =3\Rightarrow \beta =-\frac{2}{5}\in \left(-1,0\right)$