Exercises: Know the Fundamental Theorem of Algebra

For quadratic problems, show the discriminant. For root-counting, include multiplicity.

Grade 9·20 problems·~40 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-c-9

Work through problems with immediate feedback

Fluency Practice

Classify the discriminant case for $x^2 - 4x + 4 = 0$ and identify the roots.

Discriminant $= 0$ : one root $x = 2$ (multiplicity 2); total root count is $2$

Discriminant $= 0$ : one root $x = 2$ (multiplicity 1); total root count is $1$

Discriminant $> 0$ : two distinct roots

Discriminant $< 0$ : two complex roots