Solve the following quadratic equation using formula method only … - Vidyadip

Question

Solve the following quadratic equation using formula method only
$3a^2x^2 +8abx + 4b^2 = 0, a \neq 0$

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Answer

$3 a^2 x^2+8 a b x+4 b^2=0$
$ x ^2+\frac{8 b }{3 a } x +\frac{4 b ^2}{3 a ^2}=0$
$ a=1 ; b=\frac{8 b}{3 a} ; c=\frac{4 b^2}{3 a^2}$
$ D=b^2-4 a c \\ =\left(\frac{8 b }{3 a }\right)^2-4(1)\left(\frac{4 b ^2}{3 a ^2}\right) $
$=\frac{64 b^2}{9 a^2}-\frac{16 b^2}{3 a^2} $
$=\frac{64 b^2-48 b^2}{9 a^2}=\frac{16 b^2}{9 a^2} $
$ x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a} $
$ x=\frac{-\frac{8 b }{3 a } \pm \sqrt{\frac{16 b ^2}{9 a ^2}}}{2} $
$ x=\frac{-\frac{8 b}{3 a}+\frac{4 b}{3 a}}{2}, x=\frac{-\frac{8 b}{3 a}-\frac{4 b}{3 a}}{2}$
$x=\frac{-4 b}{6 a}, x=\frac{-12 b}{6 a}$
$x=-\frac{2 b}{3 a}, x=-\frac{2 b}{a} $

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