Question

1) if the roots of the equation ax^2+bx+c=0 are in the ratio 2:3, then find the condition.​

Answer 1

Answer:

$\large{\bold{8b^2=25ac}}$

Step-by-step explanation:

$ax^2+bx+c=0$

$Given \quad \alpha:\beta=2:3$

$\frac{\alpha}{\beta}=\frac{2}{3}$

WKT

$\frac{\alpha}{\beta}=\frac{-b+\sqrt{b^2-4ac}}{-b-\sqrt{b^2-4ac}}$

$\frac{2}{3}=\frac{-b+\sqrt{b^2-4ac}}{-b-\sqrt{b^2-4ac}}$

$=>-2b-2\sqrt{b^2-4ac}=-3b+3\sqrt{b^2-4ac}$

$b=5\sqrt{b^2-4ac}$

Squaring on Both Sides

$b^2=25(b^2-4ac)$

$24b^2=100ac$

$8b^2=25ac$

HOPE IT HELPS