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7.5 Roots and Zeros of a Function

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7.5 Roots and Zeros of a Function. Zeros, Factors & Roots Summary:. c is a zero of f(x) x - c is a factor of f(x) c is a root/solution of f(x) = 0 If c is real, (c,0) is an x- intercept. Fundamental Theorem of Algebra.

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slide1

7.5

Roots and Zeros of a Function

zeros factors roots summary
Zeros, Factors & RootsSummary:
  • c is a zero of f(x)
  • x - c is a factor of f(x)
  • c is a root/solution of f(x) = 0
  • If c is real, (c,0) is an x-intercept.
fundamental theorem of algebra
Fundamental Theorem of Algebra

Every polynomial equation with degree greater than zero has at least one root in the set of complex #’s.

An nth degree polynomial equation of the form P(x) = 0

  • has exactly n roots in the set of complex #’s.
  • has exactly n zeros.
state the number and type of roots
State the number and type of roots.

Example 2

Example 1

Example 5-1c

state the number and type of roots1
State the number and type of roots.

Example 4

Example 3

Example 5-1c

finding of possible zeros descartes rule of signs
Finding # of possible zeros( Descartes’ Rule of Signs)

1)Arrange terms of f(x) in descending order.

2)Find the number of sign changes in f(x).

Equals the # of positive real zeros

or

Subtracted by an even # yields the # of positive real zeros

3)Find the number of sign changes in f(-x).

Equals the # of positive real zeros

or

Subtracted by an even # yields the # of positive real zeros

4) Use a table to record all possibilities

homework
Homework
  • Page 375 # 13 – 23 odd