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=−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=−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=−5
and x=1
.

Answer 1

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

1. Set the first factor equal to zero: \[ x - 1 = 0 \] Solving for \(x\), we get: \[ x = 1 \]

2. Set the second factor equal to zero: \[ 2x + 5 = 0 \] Solving for \(x\), we subtract 5 from both sides: \[ 2x = -5 \] Now, divide both sides by 2: \[ x = -\frac{5}{2} \]

Thus, the values of \(x\) that make the quadratic equation equal 0 are \[ x = 1 \quad \text{and} \quad x = -\frac{5}{2}. \]

From the answers provided, the correct response is: The quadratic equation will equal zero when \(x\) equals negative \(\frac{5}{2}\) and \(x\) equals \(1\).