Question

Solve the following quadratic equation:

`sqrt(2)x^2 + 7x + 5sqrt(2) = 0`

Answer 1

We write, 7x = 5x + 2x as `sqrt(2)x^2 xx 5sqrt(2) = 10x^2 = 5x xx 2x` 

∴ `sqrt(2)x^2 + 7x + 5sqrt(2) = 0` 

⇒ `sqrt(2)x^2 + 5x + 2x + 5sqrt(2) = 0` 

⇒ `x(sqrt(2)x + 5) + sqrt(2)(sqrt(2)x + 5) = 0` 

⇒ `(sqrt(2)x + 5)(x + sqrt(2)) = 0` 

⇒ `x + sqrt(2) = 0` or `sqrt(2)x + 5 = 0` 

⇒ `x = -sqrt(2)` or `x = -5/sqrt(2) = -(5sqrt(2))/2` 

Hence, the roots of the given equation are `-sqrt(2)` and `(-5sqrt(2))/2`.