Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Decide whether a claimed root list accounts for all roots of a quadratic polynomial, counting multiplicity
Problem
Does the claimed root list "\(2\) only" with multiplicity not stated account for \(\text{all}~\text{roots}\) of the quadratic \(x^2-4x+4\), counting multiplicity?
Big Picture
What this problem is really about
A complete root list must account for multiplicity, not only distinct values. We’ll factor the quadratic as a perfect square, identify the single zero of its repeated factor, read the exponent as multiplicity, and compare the claimed list with the degree-two total.
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