Download 7.4 Solving Polynomial Equations

7.4 Solving Polynomial
Equations
Objectives: Solve polynomial equations.
Find the real zeros of polynomial
functions and state the multiplicity of
each.
Standard: 2.8.11.N. Solve linear, quadratic
and exponential equations.
b. 2x 3+ x2 – 6x = 0
x (2x2 + x – 6)
x (2x – 3) (x + 2)
x = 0, 3/2, and -2
c. 5x3 – 12x2 + 4x = 0
x (5x2 – 12x + 4)
x(5x – 2) (x – 2)
x = 0, 2/5, and 2
Some polynomial equations have
factors (and roots) that occur more
than once.
Use a graph, synthetic division, and factoring to
find all of the roots of the following polynomial:
b. x3+ 2x2 – 4x – 8 = 0
Use a graph, synthetic division, and factoring to
find all of the roots of the following polynomial:
c. x3 + 3x2 – 4 = 0
If x – r is a factor that occurs m times in the
factorization of a polynomial expression, P,
then r is a root with multiplicity m of the
related polynomial equation, P = 0.
In example 2 above, 3 is a root with
multiplicity 2 of the equation
x4 - 7x2 + 15x – 9 = 0.
When r is a root with even multiplicity, then
the graph of the related function will touch
but not cross the x-axis at (r, 0).
Sometimes polynomials can be factored by
using variable substitution.
Use variable substitution and factoring to find all of
the roots of the following polynomial:
x4 – 9x2 + 14 = 0
Use variable substitution and factoring to find all of
the roots of the following polynomial:
4
x
–
2
5x
–6=0
Writing Activities
Review of
Solving Polynomial Equations
Homework
Pg. 453 #12-50 even