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)
Neither of the factors, (2x−3) or (x+2), 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.
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.
The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. In other words, if \( A \times B = 0 \), then either \( A = 0 \), \( B = 0 \), or both \( A \) and \( B \) equal zero.
Applied to the quadratic equation \( (2x−3)(x+2) = 0 \), this means that in order for the entire function to equal zero, at least one of the factors, \( (2x−3) \) or \( (x+2) \), must be zero.
Therefore, 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."