Locating Real Zeros of Polynomials
MAT 102 ~ College Algebra ~ Lesson 5.3
Rational Root Theorem
 If f(x) is a polynomial of integer
coefficients, then any rational root zero
of f must be in the form of p/q, where
p is a factor of a0 (last number) and q is
a factor of the leading coefficient an
Use the rational root theorem to list all
possible rational zeros, then locate actual
zeros
f (x)  2x 3  5x 2  4x  3
2x  11x  x  30
3
2
x  x  23x  50  25x
4
3
2
Intermediate Value Theorem
 If f(x) is a polynomial, and a and b are
real numbers with a < b . If f(a) and
f(b) differ in signs, then there is at least
one point c, such that a < c < b and
f(c) = 0. That is, at least one zero of f
lies between a and b.
Show that f(x) has a zero between the
given values and approximate that zero to
the nearest tenth
f (x)  x  3x  7 between 1 and 2
3
f (x)  x  9x  14 between 1 and 4
4
2
Solve
8x  24  8x  2x  38x
4
3
2
Recommended Practice:
Pg. 401 – 404
# 1 – 24, 57 – 62, 64 – 83
Required Certification 5.3
Due: ______________
Test # 4: Wed. 12/9/09
4.4, 4.5, 4.6, 5.1, 5.2, 5.3