prove that roots of (x-a)(x-b)=h2 are always real.
 

Hello Jayanth, in the above equation coefficient of x  i.e b = -(a+b)
Coefficient of x^2 ie. a = 1
Constant term .i.e c = ab - h^2
Discriminant 
b^2 - 4 a c
(a+b)^2 - 4ab + h^2 = (a - b)^2 + h^2
So it seems the discriminant is always positive i.e D > 0
Hence only real roots. PROVED
  • 10

Hello Jayanth, in the above equation coefficient of x  i.e b = -(a+b)
Coefficient of x^2 ie. a = 1
Constant term .i.e c = ab - h^2
Discriminant 
b^2 - 4 a c
(a+b)^2 - 4ab + h^2 = (a - b)^2 + h^2
So it seems the discriminant is always positive i.e D > 0
Hence only real roots. PROVED
  • 2
What are you looking for?