Question

If $x=-3$ and $x=\frac{2}{3}$ are solution of quadratic equation ${mx}^2+7x+n=0$, find he value of $m$ and $n$.

Answer 1

$m{x}^2+7x+n=0$ --- (i)

Since $x=-3$ is a solution of (i)

So,

$m(-3{)}^2+7(-3)+n=0$

$9m+n=21$ --- (ii)

and $x=\frac{2}{3}$ is a solution of (i)

So,

$m(\frac{2}{3}{)}^2+7(\frac{2}{3})+n=0$

$4m+9n=-42$ ---- (iii)

Multiply (ii) by $9$, we get

$81m+9n=189$ ----- (iv)

subtracting (iii) by from (iv)

We get,

$m=\frac{231}{77}=3$

put $m=3$ in (ii)

$n=-6$