Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Determine how many complex roots a quadratic polynomial has, counting multiplicity
Problem
How many complex roots does \(x^2-4x+4\) have, counting multiplicity?
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What this problem is really about
The Fundamental Theorem of Algebra ties a nonconstant polynomial’s degree to its total number of complex zeros when multiplicity is included. We’ll confirm the leading quadratic coefficient is nonzero, recognize the repeated-factor structure, and count the repeated zero according to its exponent. This distinguishes distinct zero locations from the degree-based multiplicity total.
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