Question

Write a general polynomial q(z) of degree n with coefficients that are b0...bn. What are the conditions on b0...bn?

Answer 1

Answer:

$b_{0}=b_{n}$,

$b_{1}=b_{n-1}$

$b_{2}=b_{n-2}$ and so on.

Step-by-step explanation:

Let us assume that the n degree function be $q(z)=(1+z)^{n}$.

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)

Where, $b_{0}, b_{1}, b_{2},$,.........$b_{n-1}, b_{n}$ 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,

$b_{0}=b_{n}$,

$b_{1}=b_{n-1}$

$b_{2}=b_{n-2}$ and so on.

(Answer)

Answer 2

Answer:

b0=bn

b1=bn-1

b2=bn-2

This is the answer