Answer :

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.


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