Question

If f(x) = ax^2 + bx + a is divided by (x – b) a , b ≠ 0 , remainder is ‘a’ , then a is (A) b^2 (B) -1 (C) 0 (D) a + b
Explain

Answer 1

remainder when f(x) = ax^2 + bx + a is divided by (x – b), is just f(b)
so find f(b) first

Answer 2

then equate it to 'a'
f(b)=a

Answer 3

by using remainder theorem
f(b)=a*b^2+b*b+a=(a+1)b^2+a=a[given]
a+1=0------>a=-1:)