The Zero Product Property states that if the product of two factors equals zero, then at least one of the factors must equal zero. For the quadratic equation (2x - 3)(x + 2) = 0, we can apply this property.
According to the Zero Product Property, we can set each factor equal to zero:
- \( 2x - 3 = 0 \)
- \( x + 2 = 0 \)
Now we can solve these individual equations:
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From \( 2x - 3 = 0 \): \[ 2x = 3 \ x = \frac{3}{2} \]
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From \( x + 2 = 0 \): \[ x = -2 \]
Thus, the statements that must be true are:
- The equation has solutions \( x = \frac{3}{2} \) and \( x = -2 \).
- These two values are the x-intercepts of the quadratic function represented by the equation.
In summary, the statement that must be true is that the solutions to the equation are \( x = \frac{3}{2} \) and \( x = -2 \).