1. Equation: ax^2 + bx +c = 0
1.1. Concepts
1.1.1. Use α^2 +β^2, αβ as algebraic identities
1.1.2. Do not solve for α&β
1.2. Formats
1.2.1. x^2 - (α+β)x +αβ = 0
1.2.2. x^2 -(sum of alpha + beta)x+(product of alpha and beta)= 0
2. Quadratic indequalities
2.1. Keywords
2.1.1. Real & distinct
2.1.1.1. b^2 -4ac > 0
2.1.2. Equal
2.1.2.1. b^2 -4ac = 0
2.1.3. curve above/below the x-axis ( always)
2.1.3.1. b^2 -4ac < 0
2.1.4. tangent
2.1.4.1. b^2 -4ac = 0
2.1.5. no real roots
2.1.5.1. b^2 - 4ac< 0
2.1.6. meets
2.1.6.1. b^2 -4ac ≥ 0
2.1.7. Real roots
2.1.7.1. b^2 - 4ac≥0
2.2. Basic curve
2.2.1. Solve b^2-4ac = 0
2.2.2. Solve b^2-4ac < 0
2.2.3. Solve b^2-4ac > 0
2.3. Curve and line
2.3.1. Simultaneous equations
2.3.2. ax^2 + bx + c = 0
2.3.3. Solve b^2-4ac = 0
2.3.4. Solve b^2-4ac < 0
2.3.5. Solve b^2-4ac > 0
2.3.6. Solve
2.4. PROVE IT
2.4.1. cannot set b^2 -4ac > 0
2.4.1.1. Use algebra to prove
2.4.2. cannot set b^2 -4ac = 0
2.4.2.1. Use algebra to prove
2.4.3. cannot set b^2 -4ac < 0
2.4.3.1. Use algebra to prove