1 / 9

5.12 Solving Quadratic Equations by Factoring Algebra I

5.12 Solving Quadratic Equations by Factoring Algebra I. 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. Zero Factor property.

lynley
Download Presentation

5.12 Solving Quadratic Equations by Factoring Algebra I

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. 5.12 Solving Quadratic Equations by FactoringAlgebra I

  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. 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. Quadratic equation • A quadratic equation is an equation that can be written in the general form • ax2 + 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. Steps for solving quadratic equations • Write the quadratic equation in general form. • Factor the left side of the equation. • Set each factor with a variable equal to zero. • Solve each linear equation • Check each solution in the original equation

  6. Solving equations • (s-4)(s-10) = 0 • X2-144 = 0 • 6x2 + 3x = 0 • y(y-4) + 3(y-4)=0

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

  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 • x2-8x + 16=0 • Factor: (x-4)(x-4) • Set x-4 = 0 • x = 4

  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! • x2-x-2=4 so x2-x-6 = 0 • (x-3)(x+2) = 0, so x = 3 and x = -2

More Related