Roots and Coefficients; Multiple Roots

What this note covers

1. The Vieta Formulas: Where They Come From
2. Quadratic, Cubic, and Quartic Relationships
3. Worked Examples: Using Vieta Formulas
4. Forming Polynomial Equations from Root Conditions
5. Multiple Roots: Using P(x) and P'(x)
6. Finding Unknown Coefficients via Multiple Root Conditions
7. GCD of P(x) and P'(x): Detecting All Multiple Roots

7 sections · 12 key terms & formulas · 6 common mistakes