Question

find the condition that one root of ax^2+ bx+ c=0 may be more than the other by h

Answer 1

Roots are : X1 = [-b + sqrt(b^2 - 4ac)]/2a
and X2 = [-b - sqrt(b^2 - 4ac)]/2a

for one root is h more than the other root, take X1 - X2 and you will get:

sqrt(b^2 - 4ac)/a = h <---- condition