Formula Sheet

Formula	Expression
Roots	x = (-b ± sqrt(D))/(2a)
Discriminant	D = b^2 - 4ac
Sum of roots	-b/a
Product of roots	c/a
Difference of roots	sqrt(D)/\|a\|
alpha^2 + beta^2	(alpha+beta)^2 - 2alphabeta
alpha^3 + beta^3	(alpha+beta)^3 - 3alphabeta*(alpha+beta)
1/alpha + 1/beta	-b/c
alphabeta^2 + alpha^2beta	alphabeta(alpha+beta) = -bc/a^2
Vertex x-coordinate	-b/(2a)
Vertex y-coordinate	-D/(4a)
Min/Max value of f(x)	-D/(4a) (min if a>0, max if a<0)
Common root condition	(c1a2-c2a1)^2 = (a1b2-a2b1)(b1c2-b2c1)