1.  Real roots can be found from the graph (x-intercepts)  We use synthetic division with the real roots to solve for the imaginary roots  There are as many roots as the degree, so x 5 has 5 roots. Those not seen on the graph are imaginary or multiples of real roots

2.  1 › Goes straight through the zero  2 › “Touch and go” at the zero (makes a U)  3 › “S” or “Wiggles” through the zero

4.  Quadratic Formula still: › Always comes in pairs, conjugate pairs !  You will end up with a negative under the radical!!  To get rid of the negative, take out an i.

5.  If a + bi is a zero  Then a – bi is a zero  If ai is a zero  Then –ai is a zero

6. Imaginary zeros don’t cross x-axis!!!! They are imaginary you can’t see them on a graph.

7. Find all of the zeros.  Always look to see if a function will factor.  This function WILL factor.

8. f(x) = x 4 – 5x 3 + 7x 2 + 3x - 10 Find all the roots

9. Find all of the zeros of the function: x = -2 x = 1 5 roots: 3 real 2 imag. BOUNCES!

11. You Try Find All Zeros X 3 +6x 2 +20x+12

12. WS for Homework #3, 4, &7 Choose any other 3 you want **Test is next THURSDAY!**