7.6 rational zero theorem algebra ii w/ trig. rational zero theorem: if a polynomial has integer...
Post on 16-Jan-2016
229 Views
Preview:
TRANSCRIPT
7.6 Rational Zero TheoremAlgebra II w/ trig
•RATIONAL ZERO THEOREM: If a polynomial has integer coefficients, then the possible rational zeros must be a factor of the constant term divided by a factor of the leading coefficient.▫For
▫Constant term: number hanging off the end
▫Leading coefficient: an
•Remember roots and zeros are the solutions to the equation f(x)=0
11 1 0( ) n n
n nf x a x a x a x a
I. List all of the possible rational zeros of each function.
A. 4 2( ) 3 2 6 10
1, 2, 5, 10
1, 3
1 2 5 101, 2, 5, 10, , , ,
3 3 3 3
f x x x x
P
Q
B.
C.
4 3( ) 3 2 5
1, 5
1, 3
1 51, 5, ,
3 3
h x x x
P
Q
3 2( ) 10 14 36
1, 2, 3, 4, 6, 9, 12, 18
1
1, 2, 3, 4, 6, 9, 12, 18
g x x x x
P
Q
II. Find all zeros.
A. 3 2( ) 5 12 29 12f x x x x
B. 3 2( ) 4 2 20g x x x x
C. f(x) = 8x4 + 2x3 + 5x2 + 2x - 3
D. g(x) = x4 + 2x3 – 11x2 - 60
E. f(x)= x5 – 6x3 + 8x
top related