Presentation is loading. Please wait.

Presentation is loading. Please wait.

The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:

Published byPierce Haynes Modified over 9 years ago

Similar presentations

Presentation on theme: "The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:"— Presentation transcript:

1 The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:

2 List the Possible Rational Roots For the polynomial: All possible values of: All possible Rational Roots of the form p/q:

3 Find a Root That Works For the polynomial: Substitute each of our possible rational roots into f(x). If a value, a, is a root, then f(a) = 0. (Roots are solutions to an equation set equal to zero!)

4 Find the Other Roots

5 Find the Other Roots (con’t) The resulting polynomial is a quadratic, but it doesn’t have real factors. Solve the quadratic set equal to zero by either using the quadratic formula, or by isolating the x and taking the square root of both sides.

6 Find the Other Roots (con’t) The solutions to the quadratic equation: The three complex roots of the polynomial are: For the polynomial:

7 More Practice

Download ppt "The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:"

Similar presentations

Creating Polynomials Given the Zeros.. What do we already know about polynomial functions? They are either ODD functions They are either EVEN functions.

Creating Polynomials Given the Zeros.. What do we already know about polynomial functions? They are either ODD functions They are either EVEN functions.
solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.
Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x 2 + 55 =

Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =
Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!
3.7 Graphs of Rational Functions

3.7 Graphs of Rational Functions
Solving Quadratic Equations (finding roots) Example f(x) = x 2 - 4 By Graphing Identifying Solutions Solutions are -2 and 2.

Solving Quadratic Equations (finding roots) Example f(x) = x By Graphing Identifying Solutions Solutions are -2 and 2.
Bell Ringer: Find the zeros of each function.

Bell Ringer: Find the zeros of each function.
Section 7.2 – The Quadratic Formula. The solutions to are The Quadratic Formula

Section 7.2 – The Quadratic Formula. The solutions to are The Quadratic Formula
Zeros of Polynomial Functions Section 2.5 Page 312.

Zeros of Polynomial Functions Section 2.5 Page 312.
Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n≥1, then the equation f(x) = 0 has at least one complex root. Date: 2.6 Topic:

Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n≥1, then the equation f(x) = 0 has at least one complex root. Date: 2.6 Topic:
DO NOW: FACTOR EACH EXPRESSION COMPLETELY 1) 1) 2) 3)

DO NOW: FACTOR EACH EXPRESSION COMPLETELY 1) 1) 2) 3)
The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)
Roots & Zeros of Polynomials III

Roots & Zeros of Polynomials III
Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.

Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.
6.6 The Fundamental Theorem of Algebra

6.6 The Fundamental Theorem of Algebra
Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.

Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.
Solving Quadratic Equations

Solving Quadratic Equations
SOLVING QUADRATIC EQUATIONS Unit 7. SQUARE ROOT PROPERTY IF THE QUADRATIC EQUATION DOES NOT HAVE A “X” TERM (THE B VALUE IS 0), THEN YOU SOLVE THE EQUATIONS.

SOLVING QUADRATIC EQUATIONS Unit 7. SQUARE ROOT PROPERTY IF THE QUADRATIC EQUATION DOES NOT HAVE A “X” TERM (THE B VALUE IS 0), THEN YOU SOLVE THE EQUATIONS.
Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.
Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.

Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.

Similar presentations

Ads by Google