Question

Solve the following quadratic equation:

`sqrt(7)x^2 - 6x - 13sqrt(7) = 0`

Answer 1

We write, –6x = 7x – 13x as `sqrt(7)x^2 xx (-13sqrt(7)) = 91x^2 = 7x xx (-13x)`

∴ `sqrt(7)x^2 - 6x - 13sqrt(7) = 0` 

⇒ `sqrt(7)x^2 + 7x - 13x - 13sqrt(7) = 0`

⇒ `sqrt(7)x(x + sqrt(7)) - 13(x + sqrt(7)) = 0` 

⇒ `(x + sqrt(7))(sqrt(7)x - 13) = 0` 

⇒ `x + sqrt(7) = 0` or `sqrt(7)x - 13 = 0` 

⇒ `x = -sqrt(7)` or `x = 13/sqrt(7) = (13sqrt(7))/7` 

Hence, the roots of the given equation are `-sqrt(7)` and `(13sqrt(7))/7`.