Study Guide
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Quadratic Equations: Key Formulae
Core Formulae
The Quadratic Formula:
x = (−b ± √(b² − 4ac)) / 2a
Discriminant: D = b² − 4ac
- D > 0 → two distinct real roots
- D = 0 → two equal real roots
- D < 0 → no real roots
Vieta's Formulae (for ax² + bx + c = 0):
- Sum of roots: −b/a
- Product of roots: c/a
What is the discriminant?
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For 2x² + 3x − 5 = 0, find D.
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The product of roots of ax² + bx + c = 0 is:
A
−b/a
B
b/a
C
c/a
D
−c/a
By Vieta's formula, the product of roots = c/a.