Question

One of the roots of the quadratic equations 4mnx^2-6m^2x-6n^2x+ 9mn=0 (m, n not equal to zero) is​

Answer 1

$Given \: Quadratic \: equation :$

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

$\implies 2mx( 2nx - 3m) - 3n( 2nx - 3m ) = 0$

$\implies ( 2nx - 3m )( 2mx - 3n ) = 0$

$\implies ( 2nx - 3m ) = 0 \: Or \: ( 2mx - 3n ) = 0$

$\implies 2nx = 3m \: Or \: 2mx = 3n$

$\implies x = \frac{3m}{2n} \: Or \: x = \frac{3n}{2m}$

Therefore.,

$\green { \frac{3m}{2n} \: and \: \frac{3n}{2m}\: are \: roots \: of }$

$\green {\: given \:Quadratic \: equation }$

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