Problem preview

N-CN.9 Warmup M2-059-A08-V02

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 \(3i\) and \(-3i\) account for \(\text{all}~\text{roots}\) of the quadratic \(x^2+9\), counting multiplicity?

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No; 3i and -3i are too many roots for one quadratic, so the claimed list cannot be complete.

No; the roots should be 3 and -3 because x²=-9 means you take the square root and get positive and negative 3.

No; x²+9 has no roots because it cannot equal zero for any real number, so the list does not account for all roots.

Yes; solving x²+9=0 gives x=3i and x=-3i, so those are the two roots and they account for the quadratic’s degree 2 count.

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Curriculum context

Course: Math II
Standard: N-CN.9
Category: Number and Quantity
Domain: The Complex Number System
Objective: Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Problem type: Decide whether a claimed root list accounts for all roots of a quadratic polynomial, counting multiplicity