ℂ
Complex Zeros & Fundamental Theorem
AP Precalculus · Unit 1 Polynomial Functions
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Learning Objectives
FTA: degree n polynomial has exactly n roots (complex)
Complex roots come in conjugate pairs
Real zeros are x-intercepts on the graph
Visualize zeros on the complex plane
Key Theorem
Fundamental Theorem of Algebra:
Every non-constant polynomial with complex coefficients has at least one complex root.
Conjugate Root Theorem:
If a+bi is a root, then a−bi is also a root (for real coefficients).
Tags
complex zeros
FTA
conjugate pairs
AP Precalculus
Polynomial Coefficients
Adjust roots to build p(x)
Real Root r₁
-2
Real Root r₂
3
Complex a (real)
1
Complex b (imag)
2
All Zeros (degree 4)
Polynomial