basic algebra

[vaibhav101]

if the roots of the equation $$3ax^2+bx+c=0$$ , are in the ratio of 2:3, then,
A 8ac=25ab
B $$9b^2=8ac$$
C $$8b^2=9ac$$
D $$2b^2=25ac$$
E $$8b^2=25ac$$

[deloitte247]

Ratio of the roots of $$3ax^2+2bx+c=0\ is\ 2:3$$
let the roots be 2x and 3x
sum of the roots=
2x +3x = 5x
$$5x=\frac{\left(-2b\right)}{3a}$$
$$x=\frac{\left(-2b\right)}{15a}$$
product of the roots
$$2x\cdot3x=6x^2$$
$$6x^2=\frac{c}{3a}$$
$$x^2=\frac{6}{18a}$$
$$Therefore,\ \frac{4b^2}{225a^2}=\frac{c}{18a}$$
$$18\cdot4ab^2=225a^2c$$
$$9\cdot8b^2=9\cdot25ac$$
$$8b^2=25ac$$

option E is the correct answer