Question

The polynomial f(x) = x4 – 2x3 + 3x2 – ax + b = 0 when divided by (x-1) and (x+1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f(x) is divided by (x – 2)​

Answer 1

Step-by-step explanation:

When f(x) is divided by x−1 and x+1, the remainders are 5 and 19 respectively.

Therefore, f(1)=5 and f(−1)=19

1−2+3−a+b=5 and 1+2+3+a+b=19

−a+b=3 and a+b=13

Adding these two, we get,

b=8

Therefore, a=5

Substituting these values of a and b in f(x), we get,

f(x)=x

4

−2x

3

+3x

2

−5x+8

The remainder when f(x) is divided by x−2 is equal to f(2).

Therefore,

Remainder = f(2)=2

4

−2×2

3

+3×2

2

−5×2+8=10

Answer 2

Answer:

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