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

The polynomial $p(x) = x^4 + 1$ has degree $4$ and real coefficients. How many real roots does it have?

$4$ real roots (since degree $= 4$ )

$2$ real roots

$0$ real roots (all $4$ roots are complex non-real)

$1$ real root