if the roots of the equation x2-ax+b=0 are real and differ by a quantityb less than unity prove that a2-1/4

x² - ax + b = 0

if roots of the eq are (A,B) then

A+B = a , AB = b

A-B = difference of roots = [(A+B)² - 4AB]^1/2

A-B = [ a² - 4b ]^1/2

A-B = b               (given)

s0 , b = [ a² - 4b ]^1/2

 a² - b² - 4b = 0

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