**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:__

- x^2 +
4x = -4

- x^2 +
8 = 6x

- x^2 –
5x = 6

- 4a^2 =
25

- m^2 –
4m = 3

- x^2 = -3x
+ 5

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

- 12x^2 = 48

- x^2–
10 = -6x

- x^3 +
x^2 = 30x