Quadratic Equations: One-Page Formula Sheet

Quadratic Equations — formula sheet

Formulas

• x = (−b ± √D)/2a, D = b² − 4ac
• Equation with roots α, β: x² − (α+β)x + αβ = 0
• α² + β² = (α+β)² − 2αβ
• Common root condition: (c₁a₂ − c₂a₁)² = (b₁c₂ − b₂c₁)(a₁b₂ − a₂b₁)

Key ideas

• D > 0 real distinct, D = 0 equal, D < 0 complex
• Sum of roots −b/a, product c/a
• Graph opens up if a > 0
• Location of roots uses D, f(k) and the vertex

Traps to avoid

• Ignoring a = 0 case
• Forgetting conditions for both roots on one side of k
• Sign errors in symmetric expressions

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