Page 3: Advanced Applications

This final section focuses on complex applications of polynomial root-finding and factorization techniques.

Example: For W(x) = x³ - mx² + nx - 3, when x = -1 is a root, we can determine m and n values.

Highlight: The process of finding pierwiastki całkowite wielomianu (integer roots) often involves:

• Using the rational root theorem
• Analyzing factors of the constant term
• Synthetic division

Vocabulary:

• Krotność pierwiastka (Root multiplicity)
• Dzielniki (Factors)
• Rozwiązanie (Solution)

The page includes detailed examples of solving complex polynomial equations and determining multiple roots.

Page 1: Finding Polynomial Roots

This page introduces fundamental concepts of wyznaczanie pierwiastków wielomianu (finding polynomial roots) through practical examples and exercises.

Definition: A polynomial root (zero) is a value of x for which W(x) = 0.

Example: For W(x) = x - 2x³ + ax - 4, when W(2) = 16 - 16 + 2a - 4 = 0, we find a = 2.

Highlight: The process of jak obliczyć pierwiastek wielomianu involves systematic evaluation and factorization techniques.

The page demonstrates various approaches to finding pierwiastki wielomianu, including:

• Direct substitution method
• Factor theorem application
• Analysis of polynomial behavior

Vocabulary:

• Wielomian (Polynomial)
• Pierwiastek (Root)
• Miejsce zerowe (Zero)