Take 10 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
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Question
The polynomial
is of degree
of leading coefficient
and admits
distinct complex roots,
We denote by
the derivative polynomial of
Prove that for any complex number
we have:
Indice
Use the Gauss's factorization of the polynomial :
then express polynomial
as a product.
Solution
By the factorization theorem of Gauss, we have:
Iterring the calculation, we get:
This results in:
