Write a general polynomial q of z of degree n with coefficient that are b not......b n.what are the conditions on b 0...bn ?.
Answers
Step-by-step explanation:
b
0
=b
n
,
b_{1}=b_{n-1}b
1
=b
n−1
b_{2}=b_{n-2}b
2
=b
n−2
and so on.
Step-by-step explanation:
Let us assume that the n degree function be q(z)=(1+z)^{n}q(z)=(1+z)
n
.
Now this function can be expanded using binomial theorem as
(1+z)^{n}=b_{0}+b_{1}z+b_{2}z^{2}+b_{3}z^{3}+.........+b_{n-1}z^{n-1}+b_{n}z^{n}(1+z)
n
=b
0
+b
1
z+b
2
z
2
+b
3
z
3
+.........+b
n−1
z
n−1
+b
n
z
n
........ (1)
Where, b_{0}, b_{1}, b_{2},b
0
,b
1
,b
2
, ,.........b_{n-1}, b_{n}b
n−1
,b
n
are the coefficients of 1st, 2nd, 3rd,....... upto (n+1)th terms of the expansion.
The conditions for equation (1) to be valid only if n is a positive integer.
And the conditions on the coefficients are that,
b_{0}=b_{n}b
0
=b
n
,
b_{1}=b_{n-1}b
1
=b
n−1
b_{2}=b_{n-2}b
2
=b
n−2
and so on.
(Answer)