Fundamental Theorem of Algebra (Quadratic) Math Activities

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Definition

The Fundamental Theorem of Algebra (Quadratic Case) states that every quadratic polynomial (a polynomial of degree 2) with complex coefficients has exactly two solutions (roots) in the complex number system. This means that any quadratic equation in the form

has two solutions, which may be real or complex numbers.

Summary

The Fundamental Theorem of Algebra guarantees that quadratic equations always have solutions within the complex number system. Even if a quadratic equation has no real solutions (for example, when the discriminant $b^2 – 4ac$ is negative), it will still have two complex solutions. These solutions can be found using the quadratic formula:

If the discriminant is positive, the quadratic has two distinct real solutions.
If the discriminant is zero, it has one real solution (a repeated root).
If the discriminant is negative, it has two complex conjugate solutions.

This theorem ensures that quadratics always have exactly two roots in the complex number system, counting multiplicity.

Fundamental Theorem of Algebra (Quadratic) Math Activities

This is a fantastic bundle which includes 10 activities with answer guides about Fundamental Theorem of Algebra (Quadratic). All our worksheets are completely editable so can be tailored for your curriculum and target audience.

Resource Examples

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Worksheets Activities Included

•  Root Count Check
• Two Real Roots 
• One Repeated Root 
• No Real Roots, Still Two Complex Roots
• Discriminant Detective
• Conjugate Pair Match-Up
• Build a Quadratic from Given Complex Roots
• Complete the Square to Reveal Complex Roots
• Verify Roots Using Substitution
• FTA Proof-by-Example