Q. 11 E4.1( 7 Votes )
If n2 – 1 is a factor of the polynomial an4 + bn3 + cn2 + dn + e then
A. a + c + e = b + d
B. a + b + e = c + d
C. a + b + c = d + e
D. b + c + d = a + e
Answer :
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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