Download Lesson 4.2 Notes File

4.2 Real Zeros
• Finding the real zeros of a polynomial
f(x) is the same as solving the related
polynomial equation, f(x) = 0.
• Zero, solution, root
 x-intercepts
•Rational Zeros: zeros that are rational #’s
The Rational Zero Test
All possible rational zeros can be
r
determined by s where
• r is the factors of the constant
• s is the factors of the coefficient
Ex.1 a)Find all possible rational zeros of
f(x) = 2x4 + x3 -17x2 – 4x + 6
r=
s=
b) Determine the rational zeros.
Ex. 2 Find all REAL zeros of
f(x) = 2x4 + x3 - 17x2 – 4x + 6
Bounds Test: Used to determine which #’s
ALL zeros are between
• Upper bound – a #  0 that results in
the last row in synthetic division being
nonnegative.
• Lower bound – a #  0 that results in
the last row in synthetic division
alternating positive and negative.
Ex. 3 Find all real zeros of
f(x) = x6 + x3 – 7x2 - 3x + 1
a) Find all rational zeros.
r=
s=
b) Use the bounds test to find lower &
upper bounds for the zeros.
c) Use calculator to approximate the zeros.
Ex. 4 Find all real zeros of f(x) =
x7 – 6x6 + 9x5 + 7x4 – 28x3 + 33x2 - 36x + 20