FSQE - Zero Product Property (Lesson)
Zero Product Property
What is the purpose of factoring quadratic expressions? So you can solve quadratic equations! If a quadratic equation is factorable, then you can use the Zero Product Property.
Let's try using the zero product property to solve quadratic equations:
x2 = 9x + 22
First, write the equation in standard form.
x2 - 9x - 22 = 0
Now factor if possible.
(x - 11)(x + 2) = 0
x - 11 = 0 or x + 2 = 0
x = 11 or x = -2
Watch this video to try a few more:
VIDEO WAS CUT OFF...HERE IS THE REST OF THE PROBLEM...
(4x2 + 20x) - (5x + 25) = 0
4x(x + 5) -5(x + 5) = 0
(4x - 5)(x + 5) = 0
4x - 5 = 0; x = 5/4
x+ 5 = 0; x = -5
Try the following problems to see if you've got it
Zero Product Property Practice
Try the following problems to see if you've got it.
- 5x2 + 19x = -12
- 25x2 - 9 = 0
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
Now let's go back to our introduction problem.
You decide to plant a vegetable garden and you want it to take 24 square feet of planting space. You also want one side to be 2 feet longer than the other side.
Step 1: Let x represent the width of the rectangle.
Step 2: Draw a picture.
Step 3: Set up an equation.
We know A = lw, so 24 = x(x + 2)
Step 4: Solve the equation.
24 = x(x + 2)
24 = x2 + 2x
0 = x2 + 2x - 24
0 = (x + 6)(x - 4)
x + 6 = 0 or x - 4 = 0
x = -6 or x = 4
We know that the length of a side of a rectangle cannot be negative, so the width must be 4 and the length must be 6.
Step 5: Check your answer.
Width: 4
Length: 4 + 2 = 6
Area: 4 x 6 = 24
Let's try another one!
Vegetable Garden Practice
Try this one on your own:
A square and a rectangle have the same area. The length of the rectangle is 5 inches more than twice the length of the side of the square. The width of the rectangle is 6 inches less than the side length of the square. Find the side length of the square.
- What should we let x be?
- Draw a picture and label the square and rectangle.
- Since the areas of each shape are the same, what should the equation be?
- Now solve the equation.
- Since the side of a square cannot be negative, which answer must you choose?
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
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