1 / 10

Section 5.5 – The Real Zeros of a Rational Function

Section 5.5 – The Real Zeros of a Rational Function. Remainder Theorem. If f(x) is a polynomial function and is divided by x – c, then the remainder is f(c). Example:. T he remainder after dividing f(x) by (x – 4) would be -7. Section 5.5 – The Real Zeros of a Rational Function.

lanai
Download Presentation

Section 5.5 – The Real Zeros of a Rational Function

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Section 5.5 – The Real Zeros of a Rational Function Remainder Theorem • If f(x) is a polynomial function and is divided by x – c, then the remainder is f(c). • Example: The remainder after dividing f(x) by (x – 4) would be -7.

  2. Section 5.5 – The Real Zeros of a Rational Function • Factor Theorem • If f(x) is a polynomial function, then x – c is a factor of f(x) if and only if f(c) = 0. • Example: The remainder after dividing f(x) by (x + 3) would be 0.

  3. Section 5.5 – The Real Zeros of a Rational Function Rational Zeros Theorem (for functions of degree 1 or higher) (1) Given: (2) Each coefficient is an integer. If (in lowest terms) is a rational zero of the function, then p is a factor of and q is a factor of . • Theorem: A polynomial function of odd degree with real coefficients has at least one real zero.

  4. Section 5.5 – The Real Zeros of a Rational Function Rational Zeros Theorem Example: Find the solution(s) of the equation. Possible solutions: Try:

  5. Section 5.5 – The Real Zeros of a Rational Function Long Division Synthetic Division

  6. Section 5.5 – The Real Zeros of a Rational Function

  7. Section 5.5 – The Real Zeros of a Rational Function Example: Find the solution(s) of the equation. Possible solutions : Try: Try: Try:

  8. Section 5.5 – The Real Zeros of a Rational Function

  9. Section 5.5 – The Real Zeros of a Rational Function Intermediate Value Theorem In a polynomial function, if a < b and f(a) and f(b) are of opposite signs, then there is at least one real zero between a and b.

  10. Section 5.5 – The Real Zeros of a Rational Function Intermediate Value Theorem Do the following polynomial functions have at least one real zero in the given interval?

More Related