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

Answer:

$B.\ \frac{3m}{2n}$

Step-by-step explanation:

Given

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

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

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

$x = \frac{3n}{2m}\ or\ x = \frac{3m}{2n}$

From the list of given options, one of the roots of the equation is $\frac{3m}{2n}$