Name:  ______________________________                       SOLVING QUADRATIC EQUATIONS

 

NOTES:

1.      Apply the Zero Factor-Zero Product Theorem

:    Product of 2 factors is zero, if and only if one or both of the factors is 0.

;;Demostrate the Zero factor-zero product theorem for use in solving quadratic equations

;;factorzero: number number -> string

(define (factorzero x y)

  (cond

    [(and (= x 0)(= y 0)) "zero"]

    [(= x 0) "zero"]

    [(= y 0) "zero"]

    [else "Theorem says, must get zero. Application - use the addition inverse property to get zero on one side of the quadratic equation to factor and solve!"]))      

2.      Set each of the linear factors equal to zero. (Why are the factors linear?)

3.      These values are called the solution to the equation, or the “ROOTS” of the equation.

4.      Since there are 2 factors for every quadratic equation, there will be two roots for every second degree equation.

5.      For perfect square trinomials, the two linear factors are identical, so the roots (solutions) are the same.

 

PROCESS:

1.      Get all non-zero terms on one side of the equal sign using the additive inverse property.

2.      Factor the trinomial. Use “rhythm and patterns” by Lauren. See previous worksheet for process.

3.      Set each of the factors equal to zero.

4.      Solve the equations and show two solutions as a set {root1, root2}

5.      Check by substituting the solution set in the original equation.

 

Show all work (PROCESS) on notebook paper– see packet page 382 for an examples.

Record solution set here:

 

  1. x^2 + 4x = -4

 

  1. x^2 + 8 = 6x

 

  1. x^2 – 5x = 6

 

  1. 4a^2 = 25

 

  1. m^2 – 4m  = 3

 

  1. x^2 = -3x + 5

 

  1. 7x^2 + 12x = -x^3

 

  1. 12x^2 = 48

 

  1. x^2– 10 = -6x

 

  1. x^3 + x^2 = 30x