CAT Quant · Chapter Test
Quadratic Equations — 25-Question Test
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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 |
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