Download +1,0

October 21st
Happy Birthday to Thomas Schultz
& Michael Gobril & Shelby Caldwell
copyright2009merrydavidson
Warm up
1)
2)
3)
4)
Find all root’s for each function
f(x) = x – 4 x = 4
f(x) = x3 - 9x x = 0, +3
f(x) = x4 – 16 x = +2, +2i
f(x) = x3 – 5x2 – x + 5
x = +1, 5
List these roots as zero’s?
1) f(x) = x – 4 X = 4
(4,0)
2) f(x) = x3 + 9x X = 0, +3 (0,0), (+3,0)
3) f(x) = x4 – 16 X = +2, +2i
Imaginary numbers do not touch the x-axis. They
are not zero’s. (+2,0) are the only zero’s
4) f(x) = x3 – 5x2 – x + 5 X = +1, 5 (+1,0),(5,0)
2.5
What have we done already to find the
roots of a polynomial function
Factor, set each factor = 0, solve.
If you can not factor the function
use the quadratic formula if the
polynomial is a quadratic.
Why do we need the Rational
Root Theorem???
To find the roots of a polynomial
function that can not be factored of
degree higher than 2 (quadratic).
What does the Rational Root
Theorem give us???
It gives us all possible rational roots.
What does it NOT give us???
Irrational and/or Complex Roots
q
Ex 5:
Find possible rational roots.
p
2x3 + 11x2 – 7x – 6 = 0
p
constant factors
  leading coefficient factors
q
p
 1, 2,3, 6 
 

q
 1, 2 
= + (1, ½, 2, 3, 3/2, 6)
What are the possible rational roots for
the given functions.
6) f(x) = 2x4 – 3x3 + 7x – 3
 1,3 


 1, 2 
 1 3
 1, ,3, 
 2 2
7) f(x) = 3x3 + 3x2 + 2x + 4
 1, 2, 4 


 1,3 
 1 2 4
 1, , 2, , 4, 
 3 3 3
Given 1 root, find another root.
8) x = 2i
10) x = -3 - 4i
9) x = 2 + i
11) x = -3i
List the number of possible
real & imaginary roots.
f(x) = -3x7 + 4x6 – x5 + 2x4 - x3 + x2 – 4x + 10
Real
Imaginary
7
0
5
HW: WS 4-1