Transcript 6.5 Day 1

6.5 Day 1
Rational Zeros Theorem
Rational Zeros Theorem
p
q
If
is in simplest form and is a
rational root of the polynomial equation
an x  an 1 x
n
n 1
 ...a1 x  a0  0
With integer coefficients, then p must be
a factor of a0 and q must be a factor of a n
Tominaga Version
p is a factor of the constant, q is a factor of
the leading coefficient. The list of all p/q is
the list of all POSSIBLE RATIONAL
ROOTS.
Example: Find all the possible rational
zeros for the function (just p/q list).
x  5 x  2 x  24  0
3
p:
q:
p
:
q
2
Testing using synthetic division
to find a zero
•
•
•
•
Find all of the p’s
Find all of the q’s
Make a list of p/q
Use synthetic division to determine if the
number tested is a zero (if you get 0 for a
remainder, you have a root)-we will also use
graphing to help us determine which p/q’s
to use.
Find all rational zeros for the
function (only rational).
x  5 x  2 x  24  0
3
2
Find all rational zeros for the
function.
x  4x  2x  8  0
3
2
Find all zeros for the function
(this includes all rational,
imaginary, and irrational).
3x  x  x  1  0
3
2
Homework
12/17: #48 pg 339 1-12 all