Explanation

The Fundamental Theorem of Algebra states:

Every polynomial of degree n has exactly n complex roots.

This means:

• Some solutions may be complex

• Complex roots come in conjugate pairs (for real coefficients)

Example:
x² + 1 = 0 → roots ±i

Quiz

1. What does the theorem guarantee?

2. How many roots does a degree-4 polynomial have?

3. Can roots be complex?

4. Do complex roots come in pairs?

5. Why is this theorem important?

Answer Key

1. n complex roots

2. 4

3. Yes

4. Yes

5. Guarantees solutions exist