Quadratic Equations

ax^2 + bx + c = 0

X = (-b ± √(b² - 4ac)) / 2a

If p(a) = 0, then (x - a) is a factor of p(x)

If product of two numbers is zero, then at least one of them is zero

x² - (α + β)x + αβ = 0

x² + (b/a)x + (b/2a)² - (b/2a)² + c/a = 0 → (x + b/2a)² - (b² - 4ac)/4a² = 0

X = (-b ± √(b² - 4ac)) / 2a

α = (-b + √(b² - 4ac)) / 2a, β = (-b - √(b² - 4ac)) / 2a

Δ = b² - 4ac

If Δ = 0, roots are real and equal

If Δ > 0, roots are real and unequal

If Δ < 0, roots are not real