Solve the equation using the Zero Product Property.
left parenthesis 2 x minus 4 right parenthesis left parenthesis 2 x minus 1 right parenthesis equals 0
A. 2, negative one-half
B. 2, one-half
C. negative 2, 2
D. negative 2, one-half
The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero. So in this equation, we set each factor equal to zero and solve for x.
2x - 4 = 0 or 2x - 1 = 0
Solving for x in the first equation:
2x = 4
x = 2
Solving for x in the second equation:
2x = 1
x = 1/2 or one-half
Therefore, the solutions are x = 2 and x = 1/2, which can be written as option B: 2, one-half.
What are the solutions of the equation?
0 equals x squared minus 2x minus 24
A. x = 6, 4
B. x = negative 6, negative 4
C. x = negative 6, 4
D. x = 6 and negative 4
To solve the equation, we can first factor it:
0 = x^2 - 2x - 24
0 = (x - 6)(x + 4)
Now we use the Zero Product Property and set each factor equal to zero:
x - 6 = 0 or x + 4 = 0
Solving for x, we get:
x = 6 or x = -4
Therefore, the solutions of the equation are x = 6 and x = -4, which can be written as option D: 6 and negative 4.
To solve the given equation using the Zero Product Property, we first set each factor within the parentheses equal to zero, then solve for the variable.
Let's start by setting the first factor, 2x - 4, equal to zero:
2x - 4 = 0
To isolate x, we add 4 to both sides of the equation:
2x - 4 + 4 = 0 + 4
2x = 4
Next, we divide both sides of the equation by 2 to solve for x:
(2x)/2 = 4/2
x = 2
Now, let's set the second factor, 2x - 1, equal to zero:
2x - 1 = 0
To isolate x, we add 1 to both sides of the equation:
2x - 1 + 1 = 0 + 1
2x = 1
Then, divide both sides of the equation by 2:
(2x)/2 = 1/2
x = 1/2 or 0.5
Therefore, the solutions to the equation (2x - 4)(2x - 1) = 0 are:
x = 2 and x = 1/2
So, the correct answer is B. 2, one-half.