In the previous lesson you learned to solve quadratic equations by graphing. Quadratic equations can also be solved by factoring. For example, the equation 8x2 – 4x = 0 can be solved by finding factors.
To solve this equation, find values
of x that make the product 4x(2x – 1) equal to 0. Since the
product of 0 and any number is 0, at least one of the factors in the expression
must be zero.
The solutions of 8x2 – 4x = 0 are 0
and ½.
This method of solving quadratic equations uses the Zero Product Property.
We can use this property to solve any
equation that is written in the form ab = 0.
1. Solve 3x(x – 1) = 0.
Check your solution.
Alternative Solutions:
The
solutions are 0 and 1.
Recreation
Link
2. At an adventure park, you can jump
off a 26-foot cliff into a pool of water below. The equation h = –16t2 + 4t + 26 describes
your height h in feet t seconds after your jump. If you jump up
and off the cliff, what time will you pass the height of 26 feet again?
Alternative Solutions:
To
find the time at which this occurs, let h 26 and solve for t.
Check: Graph the equation and find the x-intercepts. We will graph the equation h = 4t(–4t + 1) on a graphing calculator.
The
solutions are 0 and ¼. The solution 0 represents the beginning of the jump. So,
you would return to your original location after a fourth of a second.
You will often need to factor an
equation before using the Zero Product Property to solve the equation.
Example
3. Solve x2 + 4x –
12 = 0. Check your solution.
Alternative Solutions:
The
solutions are – 6 and 2.
Example
Geometry Link
4. The length l of a rectangle is
2 feet more than twice its width w. The area of the rectangle is 144
square feet. Find the measures of the sides.
Alternative Solutions:
Sumber
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