Module 2 · Algebra
Chapter 17: Quadratic Equations
Algebra
4 topics
🎯 1 practice questions
What this chapter covers
The 4 topics below make up Quadratic Equations on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Solving & nature of roots
| Quadratic formula | x = [−b ± √(b² − 4ac)] / 2a |
|---|---|
| Discriminant | D = b² − 4ac |
| Two distinct real roots | D > 0 |
| Equal (repeated) real roots | D = 0 ⇒ x = −b/2a |
| No real roots (complex pair) | D < 0 |
Roots, building & extremes
| Sum of roots | α + β = −b/a |
|---|---|
| Product of roots | αβ = c/a |
| Equation from roots | x² − (α + β)x + αβ = 0 |
| Vertex (turning point) | x = −b/2a, value = −D/4a |
| Min if a > 0, Max if a < 0 | extreme value = c − b²/4a = −D/4a |
CAT reference
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