Quadratic Equations Online Practice

Question

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Question
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
.(1 point)
Responses

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
.
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
.
The quadratic equation will equal zero when x equals negative 5 and x equals 1 .
Remaining Attempts : 3
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Answer 1

To solve the quadratic equation \((x-1)(2x+5)=0\), we apply the Zero Product Property, which states that if the product of two factors equals zero, at least one of the factors must equal zero.

We can set each factor equal to zero:

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

Now, solving each equation:

1. For \(x - 1 = 0\): \[ x = 1 \]

2. For \(2x + 5 = 0\): \[ 2x = -5 \implies x = -\frac{5}{2} \]

Thus, the values of \(x\) that make the equation \((x-1)(2x+5)=0\) equal to zero are:

\[ x = 1 \quad \text{and} \quad x = -\frac{5}{2} \]

Therefore, the correct response is:

The quadratic equation will equal zero when \(x = -\frac{5}{2}\) and \(x = 1\).