Find all monic quadratic polynomial x square + ax + b with integer roots where 1, a, b are in A.P.

Dear  Abhisek,

x² + ax + b

for integer root discriminant must be a perfect square 

a² -4b

a = 1+d

b= 1+2d       where d is the common difference 

now putting the value

1+d² +2d -4-8d

d² -6d -3

(d-3)² -12 

now d =7,and -1 

 so a = 0  and b = -1   for d = -1 

a = 8 and b = 15        d = 7

x²  - 1    is one monic 

and x² + 8x + 15  is other

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