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...

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