Math II · N-CN.9

Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.

Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.

Concept Number and Quantity
Domain The Complex Number System
Problem Types

Problem Templates In This Objective

9 problem types are attached to this objective. The full web app handles practice, answers, hints, and walkthroughs.

Template 1

Determine how many complex roots a quadratic polynomial has, counting multiplicity

4 variants
Template 2

Verify whether a given real or complex number is a root of a quadratic by substitution

4 variants
Template 3

Write and verify a quadratic factorization from its roots

4 variants
Template 4

Identify the repeated root and its multiplicity in a quadratic of the form a(x-r)²

4 variants
Template 5

Separate quadratic root type, distinctness, and multiplicity counts

4 variants
Template 6

Find the other root of a quadratic with real coefficients when one complex root is given

4 variants
Template 7

Write a quadratic equation from two given roots

4 variants
Template 8

Decide whether a claimed root list accounts for all roots of a quadratic polynomial, counting multiplicity

4 variants
Template 9

Translate quadratic graph behavior into root values and multiplicities

4 variants