If 3 is a root of $x^2+k x-24=0$. It is also a root of
If 3 is a root of $x^2+k x-24=0$. It is also a root of
$x^2+5 x+k=0$
$x^2+k x+24=0$
$x^2-k x+6=0$
$x^2-5 x+k=0$
Solution
We have, 3 is the roots of $x^2+k x-24=0$
Then, $9+3 k-24=0$
$
3 k=15 \Rightarrow k=5
$
Also, $x^2-k x+6=0$
$
9-3 x+6=0 \Rightarrow k=5
$
Thus 3 is also the root of $x^2-k x+6=0$