(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I think I saw another thread answer this question, but I was a little lost whilst reading it.

I have just recently learned of the rational root theorem and was using it quite happily; figuring out what possibly answers went with cubic and quartic polynomials gave new meaning to guess and check.

But then I realized something strange, I am aware that, because of conjugates, complex and imaginary solutions to polynomials come in pairs. I am also aware that the amount of roots in a polynomial stem from its degree. This became confusing to me when I came across an equation that was not solved using one of the roots found with the rational root theorem.

I am confused on how it is possible for a cubic polynomial to have no rational roots, and thus, three imaginary or complex roots - even though complex and imaginary numbers must come in pairs.

I asked my teacher, but he did not know.

2. Relevant equations

This was the equation that spurred the whole confusion:

2x[tex]^{3}[/tex]-5x[tex]^{2}[/tex]-9x+13=0

this is a different one my teacher showed the class after I asked him about it:

2x[tex]^{3}[/tex]-9x[tex]^{2}[/tex]-11x+8=0

3. The attempt at a solution

I thought it was as simple as a multiplicity. But that wouldn't work. I am really at a lost here.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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

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: Cubic Polynomials

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