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we consider the polynomials f : x" + x"-1+ x"-2 + x² + x +1 .. and 9: xn-1 + 2xn-2 + (п — 2)а2 + (п - 1)ӕ + п + 3xn-3 .. where n E N* We denote by S the set of roots of the polynomial f. a) Determine the set S b) Solve in C the equation: E la – 21? = n ZESI where S1 = SU {1} C) SHow that IIzes(1 – z) = n +1 and calculate

we consider the polynomials f : x" + x"-1+ x"-2 + x² + x +1 .. and 9: xn-1 + 2xn-2 + (п — 2)а2 + (п - 1)ӕ + п + 3xn-3 .. where n E N* We denote by S the set of roots of the polynomial f. a) Determine the set S b) Solve in C the equation: E la – 21? = n ZESI where S1 = SU {1} C) SHow that IIzes(1 – z) = n +1 and calculate

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter7: Polynomial Equations And Factoring
Section: Chapter Questions
Problem 1CA
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Consider the polynomials
$f: x^{n}+x^{n-1}+x^{n-2}+\cdots+x^{2}+x+1$
and
$g: x^{n-1}+2 x^{n-2}+3 x^{n-3}+\cdots+(n-2) x^{2}+(n-1) x+n$
where $n \in N ^{*}$
We denote by $S$ the set of roots of the polynomial f.
a) Determine the set $S$
b) Solve in $\mathbb{C}$ the equation:
$$
\sum_{z \in S_{1}}|x-z|^{2}=n
$$
where $S_{1}=S \cup \{1\}$
C) SHow that $\prod_{z \in S}(1-z)=n+1$ and calculate
$$
\prod_{z \in S} g(z)
$$

Please check the attached picture for details.

Please write the complete solution.

Thanks in advance.

we consider the polynomials f : x" + x"-1 + xn-2 + + x? + x +1 .. and 9: xn-1 + (n — 2)2? + (п — 1)ӕ + п + 2xn-2 + 3xn-3 ... where n E N* We denote by S the set of roots of the polynomial f. a) Determine the set S b) Solve in C the equation: E lz – 2/² = ZES1 where S1 = SU{1} C) SHow that IIres(1 – z) = n +1 and calculate II 9(2) zES
Transcribed Image Text:we consider the polynomials f : x" + x"-1 + xn-2 + + x? + x +1 .. and 9: xn-1 + (n — 2)2? + (п — 1)ӕ + п + 2xn-2 + 3xn-3 ... where n E N* We denote by S the set of roots of the polynomial f. a) Determine the set S b) Solve in C the equation: E lz – 2/² = ZES1 where S1 = SU{1} C) SHow that IIres(1 – z) = n +1 and calculate II 9(2) zES
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