Question

Solve the following quadratic equation:

`3x^2 - 2sqrt(6)x + 2 = 0`

Answer 1

We write, `-2sqrt(6)x = -sqrt(6)x` as `3x^2 xx 2 = 6x^2 = (-sqrt(6)x) xx (-sqrt(6)x)`  

∴ `3x^2 - 2sqrt(6)x + 2 = 0` 

⇒ `3x^2 - sqrt(6)x - sqrt(6)x + 2 = 0`

⇒ `sqrt(3)x(sqrt(3)x - sqrt(2)) - sqrt(2)(sqrt(3)x - sqrt(2)) = 0` 

⇒ `(sqrt(3)x - sqrt(2))(sqrt(3)x - sqrt(2)) = 0`

⇒ `(sqrt(3)x - sqrt(2))^2 = 0` 

⇒ `sqrt(3)x - sqrt(2) = 0` 

⇒ `x = sqrt(2)/sqrt(3) = sqrt(6)/3` 

Hence, `sqrt(6)/3` is the repeated root of the given equation.