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
.
The quadratic equation will equal zero when x equals negative 1 and x equals Start Fraction 2 over 5 End Fraction .
Remaining Attempts : 3

Answer 1

To solve the equation \((x−1)(2x+5)=0\), we can apply the Zero Product Property, which states that if a product of two factors is equal to zero, at least one of the factors must be equal to zero.

Set each factor equal to zero:

1. \(x - 1 = 0\)
2. \(2x + 5 = 0\)

Solving the first equation:

1. \(x - 1 = 0\)
   \(x = 1\)

Solving the second equation:

2. \(2x + 5 = 0\)
   \(2x = -5\)
   \(x = -\frac{5}{2}\)

Therefore, the solutions are \(x = 1\) and \(x = -\frac{5}{2}\).

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.