Question

If $x=2$ and $x=3$ are roots of the equation ${3x}^2-2mx-2n=0$ find the values of $m$ and $n$.

Answer 1

$3x^2-2mx-2n=0$

$\alpha +\beta =2+3=\frac{-b}{a}=\frac{2m}{3}$

$\Rightarrow 5\times 3=2m\Rightarrow m=\frac{15}{2}$

$\alpha \beta =\left(2\right)\left(3\right)=\frac{c}{a}=\frac{-2n}{3}$

$\frac{6\times 3}{-2}=n$

$\Rightarrow n=-9$.