1.

If the difference of the roots of the quadratic equation x2 + ax + b = 0 is 1. thenprove that a2 = 4b + 1.​

Answer»

Step-by-step explanation:

Given If the difference of the roots of the QUADRATIC equation x2 - ax + b = 0 is 1. then  PROVE that a2 = 4b + 1.

  • Let α and β be the roots of the quadratic equation  
  • So  x^2 – ax + b = 0
  • Comparing with ax^2 + bx + c we get a = 1, b = - a and c = b
  • Now SUM of roots α + β = - b / a
  •                                          = -(-a) / 1
  •                                           = a
  • Product of roots = c/a
  •                           = b / 1
  •                           = b
  • According to QUESTION α – β = 1
  •                                  (α – β^2 = α + β)^2 - 4αβ
  •                                      1^2 = a^2 – 4b

Or we get a^2 = 4b + 1

Reference link will be

brainly.in/question/15299234


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