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# Find the roots of the following quadratic equations by factorisation √ 2x^2 +7x +5√ 2 =0 - Mathematics

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#### Question

Find the roots of the following quadratic equations by factorisation

sqrt2 x^2 +7x+ 5sqrt2 = 0

#### Solution 1

sqrt2 x^2 + 7x + 5sqrt2

= sqrt2 x2 + 5x + 2x + 5sqrt2

= x (sqrt2x + 5) + sqrt2(sqrt2x + 5)= (sqrt2x + 5)(x + sqrt2)

Roots of this equation are the values for which (sqrt2x + 5)(x + sqrt2) = 0

:.sqrt2x + 5 = 0 or x + sqrt2 = 0

⇒ x = (-5)/sqrt2 or x = -sqrt2

#### Solution 2

We write 7x = 5x + 2x as sqrt2x^2 xx 5sqrt2 = 10x^2 = 5x xx 2x

:.sqrt2x^2 + 7x + 5sqrt2 = 0

=>sqrt2x^2+ 5x + 2x + 5sqrt2 = 0

=> x(sqrt2x + 5) + sqrt2(sqrt2x + 5) = 0

=> (sqrt2x + 5)(x + sqrt2) = 0

=> x + sqrt2 = 0or sqrt2x + 5 = 0

=> x = -sqrt2 or x = - 5/sqrt2 = -(5sqrt2)/2

Hence the roots of the given equation are -sqrt2 and - (5sqrt2)/2

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