Based on the Zero Product Property, if either of the two factors in a quadratic equation equals zero, the entire equation equals zero. Find the values of x that make the following quadratic equation equal 0: (x−1)(2x+5)=0
.(1 point)
Responses
The quadratic equation will equal zero when x=0
and x=1
.
The quadratic equation will equal zero when x equals 0 and x equals 1 .
The quadratic equation will equal zero when x=−52
and x=1
.
The quadratic equation will equal zero when x equals negative Start Fraction 5 over 2 End Fraction and x equals 1 .
The quadratic equation will equal zero when x=−5
and x=1
.
The quadratic equation will equal zero when x equals negative 5 and x equals 1 .
The quadratic equation will equal zero when x=−1
and x=25
.
The correct answer is: The quadratic equation will equal zero when x equals 1 and x equals negative 5/2.
To find the values of x that make the quadratic equation equal to zero, you can use the Zero Product Property. According to the Zero Product Property, if either of the two factors in a quadratic equation equals zero, the entire equation equals zero.
In the given quadratic equation (x−1)(2x+5)=0, you have two factors: (x−1) and (2x+5).
To find the values of x that make the equation equal to zero, you set each factor equal to zero and solve for x.
Setting (x−1) equal to zero:
x−1=0
x=1
Setting (2x+5) equal to zero:
2x+5=0
2x=−5
x=−5/2 or -2.5
Therefore, the values of x that make the quadratic equation equal to zero are x=1 and x=−5/2 (or x=-2.5).
To find the values of x that make the quadratic equation equal to zero, we can set each factor of the equation equal to zero and solve for x.
For the first factor, setting x - 1 equal to zero:
x - 1 = 0
Adding 1 to both sides:
x = 1
For the second factor, setting 2x + 5 equal to zero:
2x + 5 = 0
Subtracting 5 from both sides:
2x = -5
Dividing both sides by 2:
x = -5/2
Therefore, the values of x that make the quadratic equation equal to zero are x = 1 and x = -5/2.