Question

One of the roots of the quadratic equation 4mnx^2 – 6m^2x – 6n^2x + 9mn = 0 (m, n ≠ 0) is a)-3m/2n b)3m/2n c)2m/3n d)-2m/3n

Answer 1

`B.\ (3m)/(2n)`

Explanation:

Given

`4mnx^2 - 6m^2x - 6n^2x + 9mn = 0\ (m, n \\eq 0)`

Required

Calculate one of the root of the equation

`4mnx^2 - 6m^2x - 6n^2x + 9mn = 0`

Factorize

`2mx(2nx - 3m) -3n(2nx - 3m) = 0`

`(2mx - 3n)(2nx - 3m) = 0`

Split equation

`2mx - 3n = 0\ or\ 2nx - 3m = 0`

Make x the subject of formula in both expressions

`2mx = 3n\ or\ 2nx = 3m`

`x = (3n)/(2m)\ or\ x = (3m)/(2n)`

From the list of given options, one of the roots of the equation is
`(3m)/(2n)`