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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

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

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

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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