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)

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=−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.

GPT-4o mini · Answer

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 to zero: $$ x - 1 = 0 $$ Solving for $x$, we get: $$ x = 1 $$ 2. Set the second factor to zero: $$ 2x + 5 = 0 $$ Solving for $x$, we subtract 5 from both sides: $$ 2x = -5 $$ Then divide by 2: $$ x = -\frac{5}{2} $$ Therefore, the solutions to the equation are $x = 1$ and $x = -\frac{5}{2}$. From the provided responses, the correct option is: **The quadratic equation will equal zero when x equals negative Start Fraction 5 over 2 End Fraction and x equals 1.**