Download presentation

Presentation is loading. Please wait.

1
Finding Rational Zeros

2
**Zeros = Solutions = Roots = x-intercepts**

Find all zeros of x2 –10x + 24 You just factor and set each factor to zero. (You knew this already!) (x – 12)(x + 2) = 0 x = 12, -2 You could also graph and see where it crosses the x-axis (x-intercepts) (You knew this already too!)

3
**Refresh. What is a Rational Number?**

A number that can be written as the ratio of two integers. Examples: It can also be an ending or repeating decimal. Examples: … …

4
**= Rational Zero Theorem**

If f(x) = anxn + … + a1x + a0 (it’s a polynomial) and the polynomial has integer coefficients, then EVERY rational zero of f has the following form: = factor of the constant term . factor of the leading coefficient

5
**= p is all of the factors of the constant term. 1, 3, 2, 4, 6, 12**

“p over q” Find the rational zeros of f(x) = x3 + 2x2 – 11x – 12 p is all of the factors of the constant term. 1, 3, 2, 4, 6, 12 q is all of the factors of the leading coefficient. This one is easy because the leading coefficient is 1 ! The only factor is: 1 = 1, 3, 2, 4, 6, 12

6
Using Still finding the rational zeros of f(x) = x3 + 2x2 – 11x – 12 1, 3, 2, 4, 6, 12 Possible Zeros: Do synthetic division until you find a zero. x x (-11) x + (–12) – 1 k-value 1 • 1 is not a zero to this function. Remainder is not zero so 1 3 -8 1 3 -8 -20

7
**Keep trying Possible Zeros**

Test x = -1. x x (-11) x + (–12) -1 • – -1 k-value -1 IS a zero to this function! Remainder IS zero so -1 -1 12 1 1 -12 Since -1 is a zero of f, then the result is a factor (x2 + x – 12) This is factorable into: (x + 4)(x – 3). The zeros are: -1 (original zero), -4, 3

8
The Nightmare Example Find the rational zeros of f(x) = 10x4 - 3x3 - 29x2 + 5x + 12 = 1, 3, 2, 4, 6, 12 1 1, 3, 2, 4, 6, 12 2 1, 3, 2, 4, 6, 12 5 1, 3, 2, 4, 6, 12 10

9
**The Nightmare Example (cont’d)**

Finding the zeros of f(x) = 10x4 - 3x3 - 29x2 + 5x + 12 With so many possible zeros, it’s worth our time to get a ballpark answer by graphing the polynomial on the calculator. -3/2 • -15 27 3 -12 10 -18 -2 8 We found the 1st Zero!

10
**= What do you need to remember? Rational Zero Theorem**

If f(x) = anxn + … + a1x + a0 (it’s a polynomial) and the polynomial has integer coefficients, then EVERY rational zero of f has the following form: factor of the constant term . factor of the leading coefficient = Rational Zero Theorem Be able to list all possible rational zeros. Then let your calculator do the rest!

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google