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=−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=−1
and x=25
.

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

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

So the values of \(x\) that make the quadratic equation equal zero are \(x = 1\) and \(x = -\frac{5}{2}\).

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