"Conjecture a classifucation rule for all irreducible polynomials of the form ax^2 + bx + c over the reals. Prove it."(adsbygoogle = window.adsbygoogle || []).push({});

I'm stuck cold at the start. classification rule ?

"Let R be an integral domain.

A nonzero f in R[x] is irreducible provided f is not a unit and in every factorization f = gh, either g or h is a unit in R[x].

So, f in R[x] is reducible over R if it can be factorised as f = gh where g,h are in R[x] with deg(g) < deg(f) and deg(h) < deg(f). And irreducible otherwise."

I have no idea where to start, I tried playing with extensions but that seems pointless in the reals.

For some p, b^2 - 4ac < 0 then p is irreducible over R. But that's not getting me anywhere.

Could someone please just give me a tiny hint/word which may shed a ray of light?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Classifcation of irreducible polynomials

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**