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Types of Zeros

Let's start small here:

If we have a 2nd degree polynomial (that's a quadratic, baby!), what are all the possible combinations of types of zeros that can happen?

-- 2 real zeros:   

  graph of a 2nd degree polynomial with two real zeros

*This includes the kissing kind like

f ( x ) = x^2

the real zeros are 0 AND 0!
0 has a multiplicity of two!

-- 2 complex zeros:

graph of a 2nd degree polynomial with 2 complex zeros

-- 1 complex and 1 real?

No way!  The complex guy needs his conjugate buddy.