The Zero Product Property states that if a product of two factors equals zero, then at least one of the factors must equal zero.
Given the quadratic equation \((2x - 3)(x + 2) = 0\), we can apply the Zero Product Property. This implies that either:
- \(2x - 3 = 0\)
- \(x + 2 = 0\)
Now, we solve each equation:
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For \(2x - 3 = 0\): \[ 2x = 3 \] \[ x = \frac{3}{2} \]
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For \(x + 2 = 0\): \[ x = -2 \]
Thus, the solutions to the quadratic equation \((2x - 3)(x + 2) = 0\) are:
- \(x = \frac{3}{2}\)
- \(x = -2\)
Therefore, the statements that must be true about the quadratic equation are that \(x\) can be either \(\frac{3}{2}\) or \(-2\).