CCSS.Math.Content.HSN-CN.C.7
The Standard
Solve quadratic equations with real coefficients that have complex solutions.
Common Core State Standards for Mathematics · The Complex Number System
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use the quadratic formula or complete the square when a negative value appears under a square root. They rewrite √(-a) as i√a, simplify, and report both conjugate roots.
What Mastery Looks Like
- Given x² + 4x + 13 = 0, a student finds -2 + 3i and -2 - 3i with clear steps. The student can substitute either root, use i² = -1, and get zero.
Common Misconceptions
- Students may stop at a negative square root and say there is no solution. They may write √(-36) as -6, forget the ± sign, or treat i² as 1. Some miss that nonreal roots occur as a conjugate pair.
How to Assess It
- Exit ticket: Solve 2x² + 4x + 10 = 0, then verify one root by substitution. Circle the step where i is introduced.
Lesson moves
Ways to Teach It
Give groups cards showing quadratic equations, discriminants, and solution pairs; have them build three-card matches and justify each match.
Ask students to explain why x² + 6x + 13 has no real zeros but still has two complex roots.
Run an error-analysis relay with worked solutions containing a missed ±, a sign error, or i² = 1; teams correct each page.
Give h(t) = t² - 4t + 8 for a machine's clearance, solve h(t) = 0, and explain why no real collision time exists.
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Printable HSN-CN.C.7 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-CN.C.7, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
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What This Unlocks
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Related Standards
- CCSS.Math.Content.HSN-CN.C
Use complex numbers in polynomial identities and equations.
- CCSS.Math.Content.HSA-REI.B.4b
Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to ...
- CCSS.Math.Content.8.EE.C.8c
Solve real-world and mathematical problems leading to two linear equations in two variables.
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