SUM · PRODUCT
For ax²+bx+c=0, sum of roots = −b/a, product = c/a. No need to solve!
sum = −b/a · prod = c/a
COMPLETE SQUARE
Move constant, add (b/2)² to BOTH sides, then take square root of both sides.
(x+b/2)² = k
FACTOR CHECK
If (x−m) is a factor of f(x), then f(m)=0. Plug m in directly!
f(m) = 0
SQUARE ROOT EQ
√(expr)=√(expr2) → square both sides, then CHECK each solution back!
always verify!
VIETA'S TRICK
ax²+bx+c=0 → roots r,s: r+s=−b/a and r·s=c/a. Skip quadratic formula!
r·s = c/a