Question

Find the roots of the quadratic equation (3x-2)square -4(3x-2)+3=0.

Answer 1

$\sf\bullet {Equation }$

$\ (3x-2)^2-4(3x-2)+3\:=\:0$

$\sf\bullet {To\: Find }$

${ \mathrm{Roots \: \: of \: \:equation}}$

$\huge{ \underline{ \underline{ \red{ \mathrm{Solution}}}}}$

${ \mathrm{⟹ \ (3x-2)^2-4(3x-2)+3\: = \: 0}}$

${ \mathrm{⟹ \ 9x^2+4-12x-12x+8+3 \: = \: 0}}$

${ \mathrm{⟹ \ 9x^2+24x+15\: = \: 0}}$

${ \mathcal{ Divide\: the \: whole\: equation\: by \: 3}}$

${ \mathrm{⟹ \ 3x^2+8x+5\: = \: = 0 }}$

${ \mathrm{⟹ \ 3x^2+3x+5x+5\: = \: 0}}$

${ \mathrm{⟹ 3x(x+1)+5(x+1)\:=\:0}}$

${ \mathrm{⟹ \ (x+1)(3x+5)\:=\:0}}$

${ \mathrm{x\: =\: -1}}$

${ \mathrm{ x\: =\: \frac{-5}{3} }}$

$\large{ \mathcal{ \boxed{ \boxed{ \purple{x\: = \: -1\: ,\:\frac{-5}{3}}}}}}$

$\large{ \mathrm{ \boxed{ \green{HOPE \: IT\: WILL\: HELP \: YOU}}}}$

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$\huge{@itzBrainlyTanuj}$

Answer 2

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