Question

EXERCISE 4.2
1. Find the roots of the following quadratic equations by factorisation:
(i) x2 – 3x - 10 = 0
(ii) 2x²+x-6=0
(iii) √2 x2+7x+ 5√2 = 0
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Answer 1

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Answer 2

Finding roots of Quadratic equations by Factorisation Method:

$i ) Given \: Quadratic \: equation : \\x^{2} - 3x - 10 = 0$

/* Splitting the middle term, we get */

$\implies x^{2} + 2x - 5x - 10 = 0$

$\implies x( x + 2 ) - 5( x + 2 ) = 0$

$\implies ( x + 2 )( x - 5 ) = 0$

$\implies x + 2 = 0 \: Or \: x - 5 = 0$

$\implies x = -2 \: Or \: x = 5$

Therefore.,

$\green { -2, 5 \: are \: roots \: of \: the }\\\green{Quadratic \: equation}$

$ii) Given \: Quadratic \: equation : \\2x^{2} + x - 6 = 0$

/* Splitting the middle term, we get */

$\implies 2x^{2} -4x + 3x - 6 = 0$

$\implies 2x( x - 2 ) + 3( x - 2) = 0$

$\implies (x-2)( 2x + 3 ) = 0$

$\implies x - 2 = 0 \: Or \: 2x + 3 = 0$

$\implies x = 2 \: Or \: 2x = -3$

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

Therefore.,

$\green { 2 , \frac{ -3}{2} \: are \: roots \: of \: }\\\green{the \:Quadratic \: equation}$

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