Based on the Zero product property, which of the following statements must be true about quadratic equation

Question

(2x - 3)(x + 2) = 0?
a Neither of the factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0
b Both factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0
c at least one of the factors, (2x - 3) or (x + 2), must equal 0 for the entire function to equal 0
d No values of x will make the function equal 0

Answer 1

The correct statement based on the Zero Product Property is:

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

According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must be equal to zero. In this case, if \((2x - 3)(x + 2) = 0\), it means that either \(2x - 3 = 0\) or \(x + 2 = 0\) (or both) must be true for the equation to hold true.