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SAT Math: The Quadratic Formula
34+ practice questions in Praczo
What you need to know
The concept, explained
- 1
The quadratic formula solves ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) / (2a).
- 2
Use it when factoring is not possible or too slow. It always works for any quadratic.
- 3
The discriminant b² − 4ac tells you how many solutions: positive → 2 real, zero → 1 (double root), negative → no real solutions.
- 4
Identify a, b, and c carefully before substituting — do not confuse signs.
- 5
The SAT sometimes asks about the discriminant without asking you to fully solve the equation.
Common mistakes
- ✗ Dropping the ± and only computing one solution.
- ✗ Misidentifying b when the equation is written in non-standard order (e.g., 3 + 2x − x² = 0 — rewrite as −x² + 2x + 3 = 0 first).
Try a sample question
SAT-style practice
How many real solutions does 2x² − 3x + 5 = 0 have?
34+ questions ready to practice
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