If he roots of the equation`12 x^2-m x+5=0` are in the ratio 2:3 then find the value of `mdot`

Answer

`m = 5 sqrt(10)`

Explanation

Let the roots be `alpha, beta`. Then,
Now, ` alpha + beta = (m)/(12)`
`rArr (2 beta)/(3) + beta = (m)/(12)`
`rArr (5beta)/(3) = (m)/(12)`
and` alpha beta = (5)/(12)`
`rArr (2beta )/(3) beta = (5)/(12)`
`rArr beta^(2) = (5)/(8)`
`rArr beta = sqrt(5//8)`
Putting the value of `beta` in (1) , we get
`(5)/(3)sqrt((5)/(8)) = (m)/(12) or m = 5 sqrt(10)` .