Since x^2+ ax + b when divided by x-1 or x+1 leaves the same remainder
So on putting x=1 and x=-1 we get the same value
1+a+b = 1-a+b
2a=0
a=0
here b can take any value as it will always get cancelled out
All such 2 digit numbers are 11,22,33,44....... upto 99
Forms an AP
So sum = n/2(a+l)
= 9/2(11+99)
Average = sum/9 = ½(11+99) = 55
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