Question

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

Answer 1

Concept : 1 Mark
Application : 1 Mark

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

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

$\Rightarrow 12-4k+2m=0$ and $27-6k+2m=0$

$\Rightarrow 12=4k-2m$ and $27=6k-2m$

Solving these two equations, we get $k=\frac{15}{2}$ and m = 9