Question

one of the roots of quadratic equation , 4mnx2-6m2x-6n2x+9mn=0​

Answer 1

$Given \: Quadratic \: equation :$

$\red{ 4mnx^{2} - 6m^{2}x - 6n^{2}x + 9mn = 0}$

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

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

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

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

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

Therefore.,

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

$\green { roots \: of \: given \: equation . }$

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