Question

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

Answer 1

$3x^2-2mx+2n=0$ .........(i)

If $x=2$, put in eqn (i),

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

$12-4m+2n=0$

$4m-2n=12$ .........(ii)

If $x=3$, put in eqn(i),

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

$27-6m+2n=0$

$6m-2n=27$ .........(iii)

Subtracting eqn (iii) from (ii),

$(4m-2n-12)-(6m-2n-27)=2m-15$

$m=\frac{15}{2}=7.5$

Put in eqn.(ii), $m=7.5$

$4\times 7.5-2n=12$

$-2n=12-30$

$n=\frac{18}{2}=9$