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

A. Neither of the factors, (2x – 3) nor (x + 2), must equal 0 for the entire function to equal 0
B. Both factors, (2x – 3) and (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

1 answer

Based on the Zero Property (also known as the Zero Product Property), if the product of two factors equals zero, then at least one of the factors must be equal to zero.

For the quadratic equation given, (2x – 3)(x + 2) = 0, this means:

  • If (2x – 3) = 0, then \(x = \frac{3}{2}\)
  • If (x + 2) = 0, then \(x = -2\)

Thus, at least one of the factors must equal zero for the entire equation to equal zero.

Therefore, the correct answer is:

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