Investigation: Zero Product Property

Investigation: Solving Quadratic Equations When solving an equation, we call the solution to the equation many different names. The following terms all mean the same thing.  Solution  X-intercept  Zero  Root

Part 1: Solve equations using the square root method. Step 1: When you solve an equation by taking the square root of both sides, ALWAYS remember that you will get 2 answers.

Example: Solve x2 = 25 by taking the square root.

Step 2: Solve each of the following. Find all roots. Leave your answers in simplest form. a. (x + 3)2 = 144 b. 5x2 – 180 = 0 c. 2x2 = 32

d. 5x2 – 40 = 0 e. 3x2 – 15 = 0 f. 9x2 = 25

2 2 2 g. 3x = 27 h. 12x – 144 = 0 i. (9 – 2x) = 40

k. 3(4x + 1)2 – 6 = 10 l. 3x2 = -18

Part 2: Solving equations by factoring Step 1: What is 3(0)? 0(6)? 7(5)(0)(82)? (x +3)(0)(32)?

Step 2: Solve for x. a. 3 + x = 0 b. 2x - 5 = 0 c. (x + 9)(6) = 0

d. 3(x – 1) = 0 e. 8(2x – 7) = 0 f. (x + 5)(x – 11) = 0

In general, if ab = 0, then either a = 0 or b = 0. We can use this property to solve quadratic equations that are factorable.

Step 3: Find the zeros of the following by factoring. And do not for get the GCF!!!! Check your answers. a. x2 = 25 b.5x2 – 20 = 0 c. 2x2 – 11x = -15

d. x2 + 7x = 18 e. 2x2 + 4x = 6 f. 16x2 = 8x

g. 10x4 + 18x3 = 4x2 h. 3x2 + 31x + 36 = 0 i. 7x2 + 14x = 0