1. Warm Up: 1) Solve: 3x 4 – 2x 3 – 37x 2 + 24x + 12 = 0 2) Graph: x 3 + x 2 – 6x = g(x)

2. 4.6 Notes: Writing Polynomial Equations

3. Conjugates Conjugates….not like the ones you do in language class In math, conjugates mean opposites. We can have conjugates for irrational numbers (roots) and complex numbers (imaginary “i”). Conjugates are opposites – same stuff just a different sign in the middle -4 + 3i and -4 – 3i3 – 7i and 3 + 7i and

4. Let’s try it…. Give the missing zeros (conjugates): 1) -1, 4i, 32) 5 – 2i, 0, 6i3), 4 – 3i, -6 Let’s write them as factors and multiply: 4) 2 + 5) -3i6) -2 + 3i

5. You try: find the conjugate, write as factors and multiply 1) 1 + 2) 6 - 3) 7i4) 9 – 4i

6. How do we write the polynomial from it’s zeros? 1) Check your zeros for values that need conjugates 2) write each zero as a factor 3) multiply your factors together (I would start with the conjugates if you have them), and the result is your polynomial.

7. Let’s try it: 1) -1, 2, 42) -6 + 9i, -8

8. Pop quiz: From your notes: 1) What is a conjugate and what two types do we use? 2) Show the work and answer for example 6: -2 + 3i