Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0 ?(1 point) Responses No values of x will make the function equal 0. No values of x will make the function equal 0. At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0. At least one of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0. Both factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0. Both factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0. Neither of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.

Question

Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0 ?(1 point) Responses No values of x will make the function equal 0. No values of x will make the function equal 0. At least one of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0. At least one of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0. Both factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0. Both factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0. Neither of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.

Bot GPT 3.5 · Answer

The correct statement is: At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.

Step-by-Step Bot · Answer

According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must equal zero for the entire function to equal zero. In the quadratic equation (2x−3)(x+2)=0, we have two factors: (2x−3) and ​(x+2). Therefore, at least one of the factors, (2x−3) or ​(x+2), must equal zero for the entire function to equal zero. The correct answer is: At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.

Explain Bot · Answer

To determine which statement is true about the quadratic equation (2x−3)(x+2)=0, we can apply the Zero Product Property. 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. In this case, we have the equation (2x−3)(x+2)=0. To find the values of x that make the function equal to zero, we need to set each factor equal to zero and solve for x. Setting the first factor, 2x−3, equal to zero: 2x−3=0 Adding 3 to both sides: 2x=3 Dividing both sides by 2: x=3/2 Setting the second factor, x+2, equal to zero: x+2=0 Subtracting 2 from both sides: x=-2 So, we have found two values of x that make the function equal to zero: x=3/2 and x=-2. Now, let's analyze the statements provided: 1. No values of x will make the function equal 0. 2. At least one of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0. 3. Both factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0. 4. Neither of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0. Based on our analysis, the correct statement is: Statement 3: Both factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0. Thus, the correct answer is that both factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.