Finding Polynomials with Integer Coefficients & \sqrt(2) + i Zero

  • Thread starter Thread starter duki
  • Start date Start date
  • Tags Tags
    Polynomials
Click For Summary

Homework Help Overview

The problem involves finding a polynomial with integer coefficients for which the complex number \(\sqrt{2} + i\) is a zero. This falls under the subject area of algebra, specifically polynomial functions and complex numbers.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to begin the problem. One suggests considering the expansion of \((\sqrt{2} + i)^2\) and \((\sqrt{2} + i)^4\) to explore potential polynomial forms. Another participant shares a polynomial they derived but questions its correctness.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to derive the polynomial. There is no explicit consensus on the correctness of the proposed polynomial, and further clarification or guidance may be needed.

Contextual Notes

Some participants mention issues with formatting, such as problems with LaTeX, which may affect the clarity of their expressions.

duki
Messages
264
Reaction score
0

Homework Statement



Find a polynomial with integer coefficient for which [tex]\sqrt(2) + i[/tex] is a zero.

Homework Equations



The Attempt at a Solution



I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?
 
Physics news on Phys.org
duki said:

Homework Statement



Find a polynomial with integer coefficient for which [tex]\sqrt(2) + i[/tex] is a zero.

Homework Equations



The Attempt at a Solution



I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?

consider (sqrt(2)+i)2...what are you left with after expanding and simplifying?
how about (sqrt(2)+i)4?
 
Ok, as an answer I got:

[tex]x^2 - 2 \sqrt{2}x + 2 - i[/tex]
Does that look right?
 
Latex isn't working, so I got

x^2 - 2sqrt(2)x + 2 - i
 

Similar threads

Maximum value of Coefficient of Fibonacci Polynomial
  • · Replies 3 ·
Replies
3
Views
2K
Finding Integer Solutions to Polynomial Equations: Can it be Done Easily?
  • · Replies 9 ·
Replies
9
Views
3K
Given a polynomial p, prove A^2-B^2 = p(1)p(-1)
  • · Replies 2 ·
Replies
2
Views
1K
Finding the coefficients of a polynomial given some restriction
  • · Replies 3 ·
Replies
3
Views
2K
Constructing cubic spline interpolation polynomials
  • · Replies 4 ·
Replies
4
Views
2K
Coefficient Matching for different series
  • · Replies 5 ·
Replies
5
Views
2K
Finding the minimal polynomial over Q
  • · Replies 27 ·
Replies
27
Views
7K
Prove that roots of trig polynomials are denumerable
  • · Replies 2 ·
Replies
2
Views
2K
Multiplicative Inverse of Polynomials with Integer Coeff.
  • · Replies 12 ·
Replies
12
Views
3K
Taylor polynomial, approximative solution of this equation
  • · Replies 3 ·
Replies
3
Views
1K