Q. 194.6( 7 Votes )

If both x+1 and x-1 are factors of ax3+x2-2x+b, find the value of a and b.

Answer :

Let, f (X) = ax3+x2-2x+b be the given polynomial.

Given (x + 1) and (x – 1) are factors of f (x).


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


a (-1)3 + (-1)2 – 2 (-1) + b = 0


-a + 1 + 2 + b = 0


-a + 3 + b = 0


b – a + 3 = 0 (i)


f (1) = 0


a (1)3 + (1)2 – 2 (1) + b = 0


a + 1 – 2 + b = 0


a + b – 1 = 0


b + a – 1 = 0 (ii)


Adding (i) and (ii), we get


b – a + 3 + b + a – 1 = 0


2b + 2 = 0


2b = - 2


b = -1


Putting value of b in (i), we get


-1 - a + 3 = 0


-a + 2 = 0


a = 2


Hence, the value of a = 2 and b = -1.


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