Warm Up. Find all zeros. Graph.. TouchesThrough More on Rational Root Theorem.

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Presentation transcript:

Warm Up. Find all zeros. Graph.

TouchesThrough

More on Rational Root Theorem

Fundamental Theorem of Algebra In the complex number system, an n th degree polynomial has precisely “n” zeros.

Find all zeros. Goes through both!

Find all zeros.

Multiplicity of 2. Just Touches.

Find all zeros.

Using the remainder theorem we see that there are NO real solutions!

Find all zeros.

Synthetic division gets you to the following: Now use the Quadratic Formula for this part.

Find all zeros.

Synthetic Division gives Multiplicity of 2

Find all zeros.

Synthetic Division gives Quadratic Formula completes it.

Complex Conjugates

Complex Zeros Always come in conjugate pairs

Write a polynomial with the given zeros: 2, i, -i

Write a polynomial with the given zeros: 3, 4i Remember – they come in pairs!

Write a polynomial with the given zeros: 4, 2-3i

Find all zeros, given that (2i) is a root.

Find all zeros, given that (1 + 3i) is a solution.

Find all zeros, given that (3 – 5i) is a solution.