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)

Question

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.
Neither 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.

Answer 1

Based on the Zero Product Property, the correct statement regarding the quadratic equation \((2x−3)(x+2)=0\) is:

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

This is because 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, the equation can be solved by setting each factor to zero:

1. \(2x - 3 = 0\)
2. \(x + 2 = 0\)

Solving these equations will provide the values of \(x\) that satisfy the original equation.