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.

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.

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.

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 property states that if the product of two expressions is equal to zero, then at least one of the expressions must be equal to zero. Therefore, one or both of the factors must equal zero to satisfy the equation.