Modern Algebra: Fields/Polynomials/Irreducible

  • Thread starter lifeonfire
  • Start date
1. The problem statement, all variables and given/known data
Prove that if F is a finite field then there is a quadratic polynomial in F[x] that is irreducible over F


2. Relevant equations



3. The attempt at a solution
To Prove:At least 1 Quadratic polynomial:Ax^2 +Bx +C not = P(x)Q(x)
I know that if P(x) is a polynomial of degree n over any field F, then P(x) = 0 has at most n distinct solutions.
Therefore a quadratic polynomial will have at least 2 zeros in any F.
But I don't what to do after that...
 

Want to reply to this thread?

"Modern Algebra: Fields/Polynomials/Irreducible" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Latest threads

Top