Answer:
[tex]B.\ \frac{3m}{2n}[/tex]
Step-by-step explanation:
Given
[tex]4mnx^2 - 6m^2x - 6n^2x + 9mn = 0\ (m, n \neq 0)[/tex]
Required
Calculate one of the root of the equation
[tex]4mnx^2 - 6m^2x - 6n^2x + 9mn = 0[/tex]
Factorize
[tex]2mx(2nx - 3m) -3n(2nx - 3m) = 0[/tex]
[tex](2mx - 3n)(2nx - 3m) = 0[/tex]
Split equation
[tex]2mx - 3n = 0\ or\ 2nx - 3m = 0[/tex]
Make x the subject of formula in both expressions
[tex]2mx = 3n\ or\ 2nx = 3m[/tex]
[tex]x = \frac{3n}{2m}\ or\ x = \frac{3m}{2n}[/tex]
From the list of given options, one of the roots of the equation is [tex]\frac{3m}{2n}[/tex]
