Download presentation

Presentation is loading. Please wait.

Published byMariah Heath Modified over 8 years ago

1
1 5.12 Solving Quadratic Equations by Factoring Algebra I

2
2 Zero-Factor Property Let a and b be real numbers, variables or algebraic expressions and factors such that a*b=0; THEN a = 0 or b= 0. This property also applies to three or more factors.

3
3 Zero Factor property This property is the primary property for solving equations in algebra For example, to solve the equation (x-1)(x+2) = 0 you can use the zero factor property to conclude that either x-1=0 or x+2 = 0. If we set the first factor to 0, x = 1; if we set the second factor to 0, x = -2 So the equation (x-1)(x+2) =0 has exactly two solutions : 1 and -2. You can check your answers.

4
4 Quadratic equation A quadratic equation is an equation that can be written in the general form ax 2 + bx + c = 0 where a, b and c are real numbers and a does not equal 0. You are going to combine your factoring skills with the Zero-Factor property to solve quadratic equations.

5
5 Steps for solving quadratic equations 1. Write the quadratic equation in general form. 2. Factor the left side of the equation. 3. Set each factor with a variable equal to zero. 4. Solve each linear equation 5. Check each solution in the original equation

6
6 Solving equations (s-4)(s-10) = 0 X 2 -144 = 0 6x 2 + 3x = 0 y(y-4) + 3(y-4)=0

7
More Examples 1) 2) 3) 4) 5) 7

8
8 Quadratic equation with a repeated solution If you have a perfect square trinomial, your factors are the same…so, you will only have one solution x 2 -8x + 16=0 Factor: (x-4)(x-4) Set x-4 = 0 x = 4

9
9 Solving a quadratic equation by factoring Solve (x+1)(x-2) =4 Don’t make the mistake of setting x+1 equal to 4. You must first satisfy the zero property rule, so you need to do FOIL and then factor and set to zero! x 2 -x-2=4 so x 2 -x-6 = 0 (x-3)(x+2) = 0, so x = 3 and x = -2

Similar presentations

© 2023 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