Question

please answer this question

Answer 1

a x² + b x + c = 0.
  roots are  α and β.
  given  α - β = 2    --- (1)
  also   α + β = -b/a   ---(2)
            α β = c/a    --- (3)

(1) and (2) ==>  2α = 2 - b/a = (2a -b)/a
Substitute in    (2):   β = -b/a - (2a - b)/2a  = -1 - b/2a = -(2a +b)/2a

(3) ==>  -(2a - b) (2a + b) / (4a²) = c/a
               b² - 4 a² = 4 a c
                 b² = 4a (a +c)