ACT Preparation / Unit 11 ACT 1005 short lesson, about 20 seconds
The Discriminant
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The idea
The discriminant, b² − 4ac, counts the real solutions: positive gives two, zero gives one repeated solution, and negative gives none real, only two complex ones.
In practice
x² + 4x + 5: 16 − 20 = −4, so no real solutions; the parabola misses the x-axis.
Where people slip
Compute the discriminant alone when the question asks how many solutions, not what they are.
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