Question

solve:3x²+10x-8=0. ​

Answer 1

$\large\bf\underline\red{Answer \: :-}$

Given equation : 3x² + 10x - 8

$\sf\implies{x {}^{2} + 10 - 24 = 0} \\ \\ \sf\implies{x {}^{2} + 12x - 2x - 24 = 0} \\ \\ \sf\implies{x(x + 12) - 2(x + 12) = 0} \\ \\ \sf\implies{(x + 12)(x - 2) = 0} \\ \\ \sf\implies{x + 12 = 0 } \\ \sf\implies{x - 2 = 0} \: \: \\ \\ \sf\implies{x = - 12} \\ \sf\implies{x = 2} \: \: \: \: \: \:$

x = -12 and x = 2 are the roots of 3x² + 10x - 8.

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Answer 2

$\bigstar\:\sf\underline{\red {Question}}:$

⠀⠀ ⠀ ⠀• solve: 3x²+10x-8=0. ​

$\bigstar\:\sf\underline{\red {Solution}}:$

$\longmapsto 3x^2 + 10x -8 = 0 \\\\ \mapsto\textsf{ Split the middle term } \\\\\implies 3x^2 + 12x - 2x - 8=0 \\\\\longmapsto \textsf{Combine like terms}\\\\\implies\sf 3x(x+4)-2(x+4) =0\\\\\implies (3x-2)(x+4) =0 \\\\\implies \sf 3x-2=0 \:\:\:\:OR \:\:\:\:\: x+4=0 \\ \\ \implies \sf x = \frac{2}{3} \:\:\:\:OR \:\:\:\:\: x = -4 \\\\\implies x = \pink{\frac{2}{3} , -4 }$

$\large\sf\underline{Therefore,}$
$\textsf{Value of x is 2/3 or -4}$
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$\\\bigstar\:\sf\underline{\red {Verification}}:$
Put the value of x in given Equation.
⠀ ⠀• Putting x = -4.
$\longmapsto 3x^2 + 10x -8 = 0 \\ \\ \implies\sf 3(-4)^2 + 10(-4) -8 = 0 \\\\\implies\sf 3(16)-40-8 = 0 \\ \\\implies \sf 0=0 \\ \bf L.H.S=R.HS.$
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⠀ ⠀• Putting x = 2/3
$\longmapsto 3x^2 + 10x -8 = 0 \\\\\implies 3\times(\frac{2}{3})^2 + 10\times\frac{2}{3} -8 = 0 \\\\\implies \sf 3\times(\frac{4}{9}) + 10\times\frac{2}{3} -8 = 0\\\\\implies \sf \frac{12}{9} + \frac{20}{3} -8 = 0\\\\\implies \sf \frac{4}{3} + \frac{20}{3} -8 = 0 \\\\\implies 8 -8 = 0 \\\\\implies 0=0 \\\bf L.H.S.= R.H.S$

$\large\:\:\:\:\: \green{\underline{verified!!}}$