Question

If $2$ and $3$ are zeros of polynomial $3x^2-2kx+2m$, then what is the value of $m$?

Answer 1

For a quadratic polynomial $a{x}^2+bx+c$,
the sum of the zeros $=\frac{-b}{a}$ and product of the zeros $=\frac{c}{a}$

Here, given polynomial is $3x^2-2kx+2m$ and zeros are $2$ and $3$
Thus,
$2+3=\frac{-(-2k)}{3}$
$=>5=\frac{2k}{3}$

$=>2k=15$

$=>k=\frac{15}{2}$ and $2\times 3=\frac{2m}{3}$

$=>6\times 3=2m$
$=>m=9$

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