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=−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=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=−1
and x=25
.
The quadratic equation will equal zero when x equals negative 1 and x equals Start Fraction 2 over 5 End Fraction .

The quadratic equation will equal zero when x=−5
and x=1
.

Answer 1

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

1. \(x - 1 = 0\)

   • Adding 1 to both sides gives: \[ x = 1 \]

2. \(2x + 5 = 0\)

   • Subtracting 5 from both sides gives: \[ 2x = -5 \]
   • Dividing both sides by 2 gives: \[ x = -\frac{5}{2} \]

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

The correct response is: The quadratic equation will equal zero when x equals negative Start Fraction 5 over 2 End Fraction and x equals 1.