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 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. 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. 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. No values of x will make the function equal 0.

Answer 1

Based on the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must equal zero. Therefore, for the quadratic equation \((2x-3)(x+2)=0\), at least one of the factors must equal zero for the entire equation to hold true.

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.

This means that if we solve the equation, we will find values for \(x\) that make either \(2x-3 = 0\) or \(x+2 = 0\).