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)

Answer 1

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

The given quadratic equation is:

(2x−3)(x+2)=0

According to the Zero Product Property, for this equation to hold true, at least one of the parentheses must equal zero. Therefore, we have two possible solutions:

1. 2x - 3 = 0
2. x + 2 = 0

Solving each equation for x gives us:

For 2x - 3 = 0:
2x = 3
x = 3/2
x = 1.5

For x + 2 = 0:
x = -2

So the two solutions to the quadratic equation (2x−3)(x+2)=0 are x = 1.5 and x = -2. This means that for the given product to be zero, one or both of the values 1.5 and -2 must be the value of x.