The zero product property quick check

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) At least one of the factors (2x - 3) or (x + 2) must equal 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 No values of x will make the function equal 0 Both factors (2x - 3) * or(x + 2) must equal for the entire function to equal 0

Answer 1

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

In the case of the quadratic equation \((2x - 3)(x + 2) = 0\):

1. At least one of the factors must equal 0: This statement is true. For the equation to hold, either \(2x - 3 = 0\) or \(x + 2 = 0\) must be true.

2. Neither of the factors must equal 0: This statement is false. We expect at least one factor to be zero for the entire product to equal zero.

3. No values of x will make the function equal 0: This statement is also false because there are values of \(x\) that will make the function equal to zero.

4. Both factors must equal 0: This statement is false. It is not necessary for both factors to be zero simultaneously; only one needs to be zero for the product to be zero.

Thus, the correct answer is: At least one of the factors (2x - 3) or (x + 2) must equal 0 for the entire function to equal 0.