Based on the zero product property which statement must be true about this equation

Question

(2x-3)(x+2)=0

Answer 1

Based on 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 equation \((2x - 3)(x + 2) = 0\), this means that either:

1. \(2x - 3 = 0\) or
2. \(x + 2 = 0\)

Solving these equations:

1. For \(2x - 3 = 0\): \[ 2x = 3 \implies x = \frac{3}{2} \]

2. For \(x + 2 = 0\): \[ x = -2 \]

Thus, the statements that must be true about this equation are that either \(x = \frac{3}{2}\) or \(x = -2\). In summary, the solutions to the equation \((2x - 3)(x + 2) = 0\) are \(x = \frac{3}{2}\) and \(x = -2\).