Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x - 3) (x + 2) = 0

Question

A. At least one of the factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0
B. No values of x will make the function equal 0
C. Both factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0
D. Neither of the factors, (2x - 3) or (x + 2), 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:

A. At least one of the factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0.

This is because the Zero Product Property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

To clarify the other options:

• B. No values of x will make the function equal 0 - This is false because there are values of x that make the function equal to 0.
• C. Both factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0 - This is false because it's sufficient for only one of the factors to equal 0.
• D. Neither of the factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0 - This is false because at least one factor must equal 0 for the product to equal 0.