Question

There are no results for Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0 ( 2 𝑥 − 3 ) ( 𝑥 + 2 ) = 0 ?(1 point) Responses Both factors, (2x−3) ( 2 𝑥 − 3 ) and ​(x+2)​( 𝑥 + 2 ) , must equal 0 for the entire function to equal 0. Both factors, left parenthesis 2 x minus 3 right parenthesis and left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0. Neither of the factors, (2x−3) ( 2 𝑥 − 3 ) nor ​(x+2)​( 𝑥 + 2 ) , must equal 0 for the entire function to equal 0. Neither of the factors, left parenthesis 2 x minus 3 right parenthesis nor 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. No values of x will make the function equal 0. At least one of the factors, (2x−3) ( 2 𝑥 − 3 ) or ​(x+2)​( 𝑥 + 2 ) , must equal 0 for t

Answer 1

Based on the Zero Product Property, if the product of two factors equals zero, at least one of those factors must equal zero.

For the quadratic equation \((2x−3)(x+2)=0\), this means:

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

Thus, the correct statement among the provided options is:
**Both factors, \( (2x−3) \) and \( (x+2) \), must equal 0 for the entire function to equal 0.**

This can be interpreted as:
**At least one of the factors, \( (2x−3) \) or \( (x+2) \), must equal 0 for the entire function to equal 0.**

Therefore, among the statements you provided, the correct one is:
**At least one of the factors, \( (2x−3) \) or \( (x+2) \), must equal 0 for the entire function to equal 0.**