Question

Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.

Answer 1

The given equation is `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0

⇒ `x^2 - sqrt(3)x - x + sqrt(3)` = 0

⇒ `x(x - sqrt(3)) - 1(x - sqrt(3))` = 0

⇒ `(x - 1) (x - sqrt(3))` = 0

⇒ `(x - 1)` = 0 or `(x - sqrt(3))` = 0

x = 1 or x = `sqrt(3)`

Hence, x = 1, `sqrt(3)` are the roots of the given quadratic equation.