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)%0D%0AResponses%0D%0A%0D%0ABoth factors, (2x−3) or %E2%80%8B(x+2), must equal 0 for the entire function to equal 0.%0D%0ABoth 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.%0D%0A%0D%0ANeither of the factors, (2x−3) or %E2%80%8B(x+2), must equal 0 for the entire function to equal 0.%0D%0ANeither 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.%0D%0A%0D%0ANo values of x will make the function equal 0.%0D%0ANo values of x will make the function equal 0.%0D%0A%0D%0AAt least one of the factors, (2x−3) or %E2%80%8B(x+2), must equal 0 for the entire function to equal 0.

Answer 1

The correct statement based on the Zero Product Property for 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 statement is true because the Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Thus, you can set each factor equal to zero to find the solutions for \(x\).