Question

One of the roots of the quadratic equation 4mnx2 – 6m2x – 6n2x + 9mn = 0 (m, n ≠ 0) is

Answer 1

Given :

Equation => 4mn$x^2$ – 6$m^2$x – 6$n^2$x + 9mn = 0

Condition => m ≠ 0 and n ≠ 0

To find :

Roots of the given quadratic equation .

Solution :

4mn$x^2$ – 6$m^2$x – 6$n^2$x + 9mn = 0

taking 2mx in common from the first two terms and 3n from last two terms ,

2mx ( 2nx - 3m ) - 3n ( 2nx - 3m )

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

=> x = 3m/2n  or x = 3n/2m

Roots of the given quadratic equation are 3m/2n and x = 3n/2m where , m ≠ 0 and n ≠ 0 .

Answer 2

Given : 4mnx² -6m²x - 6n²x  + 9mn = 0

To find : Roots

Solution:

4mnx² -6m²x - 6n²x  + 9mn = 0

=> 4mnx² -6n²x - 6m²x  + 9mn = 0

=> 2nx(2mx - 3n)  - 3m(2mx - 3n) = 0

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

=> 2mx - 3n = 0  

=> x = 3n/2m

2nx - 3m = 0

=> x = 3m/2n

roots are 3n/2m , 3m/2n

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