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

Question

.(1 point)
Responses

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=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=−1
and x=25
.

Answer 1

To solve the equation \((x - 1)(2x + 5) = 0\) using the Zero Product Property, we need to set each factor equal to zero.

1. Set the first factor equal to zero: \(x - 1 = 0\) \[ x = 1. \]

2. Set the second factor equal to zero: \(2x + 5 = 0\) \[ 2x = -5 \] \[ x = -\frac{5}{2}. \]

Thus, the values of \(x\) that make the quadratic equation equal to zero are: \[ x = 1 \] and \[ x = -\frac{5}{2}. \]

From the options given, the correct answer is:

The quadratic equation will equal zero when x equals negative 5 over 2 and x equals 1.