find the values of a and b so that (x+1) and(x-1)are factors of x^4+ax^3-3x^2+2x+b

Asked by Anishma Joseph | 15th Jul, 2013, 07:05: PM

Expert Answer:

f(x) = x^4+ax^3-3x^2+2x+b  
 
Now, since (x+1) and (x-1) are a factor of f(x)
Hence, f(1) = 0 and f(-1) = 0
f(1) = 1+a-3+2+b = 0
a+b = 0
a = -b
 
Also, f(-1) = 0
1-a-3-2+b = 0
b-a-4 = 0
b+b-4 = 0 (substituting the value of a)
2b = 4
b = 2
Hence a = -2

Answered by  | 15th Jul, 2013, 10:34: PM

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