Q11 of 82 Page 130

If n2 – 1 is a factor of the polynomial an4 + bn3 + cn2 + dn + e then

For the polynomial an4 + bn3 + cn2 + dn + e, we have n2 – 1 is a factor.


So, n2 – 1 = 0 is the root of the polynomial.


(n – 1)(n + 1) = 0


n = -1 or 1 are the roots of the given polynomial.


Now, when n = 1, we have:


a(1)4 + b(1)3 + c(1)2 + d(1) + e = 0


a + b + c + d + e = 0 ……... (1)


Now, when n = -1, we have:


a(-1)4 + b(-1)3 + c(-1)2 + d(-1) + e = 0


a – b + c – d + e = 0


a + c + e = d + b


Hence the correct option is (a).

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