Let the quadratic equation is 

ax² + bx+ c = 0

Let α and β are the two zeroes of this polynomial then 

α + β = -b/a and 

α * β = c/a

Now 

      ax² + bx+ c = 0

=> x² + (b/a)x + c/a = 0

=> x² - (α + β)x + (α * β) = 0    {b/a = -(α + β) and c/a = α * β}