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value of discriminant: b² - 4ac > 0
2 real zeros; 2 x-ints
if a perfect square
rational
if not perfect square
irrational
b²-4ac < 0
2 imaginary zeros; no x-ints
b² - 4ac = 0
1 real solution (same solution twice); vertex on x-axis
Summary
>0 —> 2 real zeros, 2 x-ints
<0 —> 2 imaginary zeros, no x-ints
=0 —> 1 real solution, vertex on x-axis