Question

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

Answer 1

$\cos A=\frac{2}{5}$ $\sin A=\pm \frac{\sqrt{21}}{5}$ $\because ({\cos }^{2}A+{\sin }^{2}A=1)$

$\tan A=\frac{\pm \sqrt{21}}{2}$

$\therefore 4+4{\tan }^{2}A=4+\frac{4\times 21}{4}=25$