Question

Find the roots of quadratic equations by factorisation:
√2 x2 + 7x + 5√2=0
​

Answer 1

$\huge{\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}$

√2 x^2 + 7x + 5√2=0

Considering the L.H.S. first,

⇒ √2 x^2 + 5x + 2x + 5√2

⇒ x (√2x + 5) + √2(√2x + 5)

= (√2x + 5)(x + √2)

The roots of this equation, √2 x^2 + 7x + 5√2=0 are the values of x for which (√2x + 5)(x + √2) = 0

Therefore, √2x + 5 = 0 or x + √2 = 0

⇒ x = -5/√2 or x = -√2

Answer 2

√2 x^2 + 7x + 5√2 = 0

=> √2 x^2 + 5x + 2x + 5√2 = 0

=> x(√2 x + 5) + √2(√2 x + 5) = 0

=> (x + √2) (√2 x + 5) = 0

=> x = -√2 , -5/√2