Find the value is of a and b, so that (x+1) and (x-1) are factors of x4+ax3-3x2+2x+b.
Let, f (x) = x4+ax3-3x2+2x+b be the given polynomial
From factor theorem
If (x + 1) and (x – 1) are factors of f (x) then f (-1) = 0 and f (1) = 0 respectively.
f (-1) = 0
(-1)4 + a (-1)3 – 3 (-1)2 + 2 (-1) + b = 0
1 – a – 3 – 2 + b = 0
b – a – 4 = 0 (i)
Similarly, f (1) = 0
(1)4 + a (1)3 – 3 (1)2 + 2 (1) + b = 0
1 + a – 3 + 2 + b = 0
a + b = 0 (ii)
Adding (i) and (ii), we get
2b – 4 = 0
2b = 4
b = 2
Putting the value of b in (i), we get
2 – a – 4 = 0
a = -2
Hence, a = -2 and b = 2.