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

Question

(3x + 4) (x-2) = 0
A. Both factors (3x+4) and (x-2) must equal 0 for the entire function to equal 0
B. No values of x will make the function equal to 0
C. Neither of the factors (3x+4) or (x-2) must equal 0 for the entire function to equal 0
D. At least one of the factors (3x+4) or (x-2) must equal 0 for the entire function to equal 0

Answer 1

The correct statement based on the zero product property is:

D. At least one of the factors (3x+4) 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 is zero, at least one of the factors must be equal to zero. This means that for the equation \((3x + 4)(x - 2) = 0\) to hold true, either \(3x + 4 = 0\) or \(x - 2 = 0\) (or both) must be true.