Question

Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The Zero Product Property states that if the product of two factors is equal to zero, then at least one of the factors must be zero. Therefore, in the equation (2x-3)(x+2) = 0, either 2x-3 = 0 or x+2 = 0 must be true.

Answer 2

[AI-generated answer — Step-by-Step Bot]

According to the Zero Product Property, if the product of two factors is equal to zero, then at least one of the factors must equal zero. In the given quadratic equation (2x−3)(x+2)=0, we have two factors: (2x−3) and (x+2). Therefore, in order for the product to be equal to zero, at least one of these factors must be equal to zero.

Setting (2x−3) equal to zero, we can solve for x:

2x - 3 = 0
2x = 3
x = 3/2

Setting (x+2) equal to zero, we can solve for x:

x + 2 = 0
x = -2

Therefore, the values of x that satisfy the equation (2x−3)(x+2)=0 are x = 3/2 and x = -2.

Answer 3

[AI-generated answer — Explain Bot]

To determine which statement is true about the quadratic equation (2x−3)(x+2)=0 using the Zero Product Property, we need to understand what the Zero Product Property is.

The Zero Product Property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

In the given equation (2x−3)(x+2)=0, we have two factors: (2x−3) and (x+2).

To find the values of x that satisfy the equation, we set each factor equal to zero and solve for x.

1. Set (2x−3) equal to zero:

2x−3 = 0
Add 3 to both sides:
2x = 3
Divide both sides by 2:
x = 3/2 or 1.5

2. Set (x+2) equal to zero:

x+2 = 0
Subtract 2 from both sides:
x = -2

Now we have found two values of x that satisfy the equation: x = 1.5 and x = -2.

Based on the Zero Product Property, the statement that must be true about the quadratic equation (2x−3)(x+2)=0 is that the values of x that make the equation true are x = 1.5 and x = -2.