Worked example
Practice set: x² − 9 = 0; x² − 6x + 9 = 0; 2x² + x − 3 = 0
- Answers: ±3; 3 repeated; 1 or −3/2.
- Record the discriminant for each equation.
- Explain why the number of distinct real roots matches its sign.
Guided practice
Choose a method, then prove your roots work.
Practice factoring, discriminants and the quadratic formula with answers you can verify.
Classify each quadratic before solving: look for a common factor, easy integer factors, a perfect square or a formula-friendly form. Finish by checking every root.
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