Cue Column:

• Sum of roots?
• Product of roots?
• How to form equation from roots?

Note Column: If alpha, beta are roots of $ax^2$ + bx + c = 0: alpha + beta = -b/a, alpha * beta = $\frac{c}{a}$. To form a quadratic with roots alpha, beta: $x^2$ - (alpha+beta)x + alphabeta = 0. These formulas allow computing symmetric expressions without finding individual roots. Key derived formulas: alpha^{2+beta}^2 = (alpha+beta)^2 - 2alphabeta, alpha^{3+beta}^3 = (alpha+beta)^3 - 3alphabeta(alpha+beta).

Summary: Vieta's formulas connect coefficients to roots. They are the primary tool for computing root expressions and forming new equations.