The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
If the roots of the equation `3ax^(2)+ 2bx + c = 0` are in the ratio 2:3 , then which one of the following is correct ?

Options

A. `8ac=25b`
B. `8ac=9b^(2)`
C. `8b^(2)=9ac`
D. `8b^(2) = 2 5ac`

Answer

D

Explanation

Let roots of equation be `2alpha and 3 alpha `
` 2alpha + 3 alpha = - (2b)/(3a)`
` rArr alpha= (-2b)/(15a)" "`…(i)
` 2alpha . 3 alpha = c/(3a) rArr alpha^(2) = c/18a" "`…(ii)
Now, put value of `alpha` in equation (ii)
` :. ((-2b)/(15a))^(2) = c/(18a) rArr (4b^(2))/(225a^(2) )=c/18a`
`rArr 8b^(2) = 25 ac`