Let the quadratic equation is 

ax² + bx + c = 0

Let α and β are the roots of the quadratic equation

Now,

α + β = -b/a .............1

and αβ = c/a

Now (α - β)² = (α + β)² - 4αβ 

=> α - β = √{(α + β)² - 4αβ} .......2 

Solve eqaution 1 and 2, we will get the value of α and β