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SAT Math: Using the Discriminant
28+ practice questions in Praczo
What you need to know
The concept, explained
- 1
The discriminant sits under the square root in the quadratic formula: b² - 4ac. It tells you the number of real solutions (x-intercepts) a quadratic has.
- 2
If b² - 4ac > 0, there are 2 real solutions.
- 3
If b² - 4ac = 0, there is exactly 1 real solution (the parabola touches the x-axis at exactly its vertex).
- 4
If b² - 4ac < 0, there are 0 real solutions (the parabola never touches the x-axis).
Common mistakes
- ✗ Forgetting to properly align the equation to ax² + bx + c = 0 before identifying a, b, and c.
- ✗ Calculating the entire quadratic formula when the question only asks HOW MANY solutions exist.
Try a sample question
SAT-style practice
How many real solutions does the equation 2x² - 4x + 5 = 0 have?
28+ questions ready to practice
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