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more than zero and perfect square
2, real, different, rational (crosses x axis twice, factorable)
more than zero and NOT perfect square
2, real, different, irrational (crosses x axis twice, not factorable)
negative
imaginary (does not cross x-axis, not factorable)
equal to 0
1 double root, multiplicity of 2 (touches x-axis once, factorable)