Question

$solve \: the \: quadratic \: equations \: by \: facctorzation : \: \\ (i) \: x {}^{2} + 6x + 5 = 0 \\ (ii) \: 8x {}^{2} - 22x - 21 = 0$
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Answer 1

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Answer 2

$(i) \: Solution : \: \: \: \: \: We, \: have \: \\ x {}^{2} + 6x + 5 = 0 \\ ⇒x {}^{2} + 5x + x + 5 = 0 \\ ⇒x(x + 5) + (x + 5) = 0 \\ ⇒(x + 5)(x + 1) = 0 \\ ⇒x + 5 = 0 \: or \: x + 1 = 0 \\ ⇒x = - 5 \: or \: x = - 1 \\ Thus, \: \: x = - 5 \: and \: x = - 1 \: are \: two \: roots \: of \: the \: given \: equation .\\ \\ (ii) \: We, \: have \: 8x {}^{2} - 22x - 21 = 0 \\ ⇒8x {}^{2} - 28x + 6x - 21 = 0 \\ ⇒4x(2x - 7) + 3(2x - 7) = 0 \\ ⇒(2x - 7)(4x + 3) = 0 \\ ⇒2x - 7 = 0 \: or \: 4x + 3 = 0 \\ ⇒x = \frac{7}{2} \: or \: x = \frac{ - 3}{4} \\ Thus, \: x = \frac{7}{2} \: and \: x = \: \frac{ - 3}{4} are \: two \: roots \: of \: given \: equation.$