Question

If $x=2$ and $x=3$ are roots of the equation $3x^2-2kx+2m=0$, find the value of $k$ and $m$.

Answer 1

Since $x=2$ and $x=3$ are roots of the equation $3x^2-2kx+2m=0$

for $x=2$

$\therefore 3\times 2^2-2k\times 2+2m=0$

$\Rightarrow 12-4k+2m=0$

$\Rightarrow 12=4k-2m$......Equation (1)

for $x=3$

$\therefore 3\times 3^2-2k\times 3+2m=0$

$\Rightarrow 27-6k+2m=0$

$\Rightarrow 27=6k-2m$.....Equation (2)

Subtracting equation (1) from (2) we get,

$15=2k$

$\therefore$ $k=\frac{15}{2}$

Putting this value in equation (1) we get,

$m=9$

$\therefore$ $k=\frac{15}{2}$ and $m=9$