If f(x) = x4- 2x3+3x2-ax+b ids divided by x-1 and x+1 the remainders are 5 and 19 respectively ,then find a and b .
f(x)=x4-2x3+3x2-ax+b
When f(x) is divided by (x-1)
it leaves a remainder 5
f(1)=5
14-2*13+3*12-a*1+b=5
1-2+3-a+b=5
2-a+b=5
-a+b-3=0 ..(1)
When f(x) is divided by (x+1)
it leaves a remainder 19
f(-1)=19
(-1)4-2(-1)3+3(-1)2-a(-1)+b
=19
1+2+3+a+b=19
a+b-13=0 ..(2)
Equating 1 and 2
-a+b-3=a+b-13
-3+13=2a
a=10/2
a=5
From 1
-a+b-3=0
-5+b-3=0
b=8