Question

If the roots of the equation $a{x}^2+bx+c=0$ are in the ratio $2:3$, then find the condition

Answer 1

Here $m=2$ and $n=3$

$\Rightarrow {(m+n)}^{2}ac=mn{b}^2$

$\Rightarrow {(2+3)}^{2}ac=2\times 3b^2$

$\Rightarrow {\left(5\right)}^{2}ac=6b^2$

$\Rightarrow 25ac=6b^2$

The condition is $25ac=6b^2$