To determine whether 3 and 4 are solutions to the quadratic equation \(x^2 - 7x + 12 = 0\), we can substitute each value into the equation and see if it holds true.
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Testing \(x = 3\): \[ 3^2 - 7(3) + 12 = 9 - 21 + 12 = 9 - 21 + 12 = 0 \] So \(x = 3\) is a solution.
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Testing \(x = 4\): \[ 4^2 - 7(4) + 12 = 16 - 28 + 12 = 16 - 28 + 12 = 0 \] So \(x = 4\) is also a solution.
Since both values satisfy the equation, the correct answer is:
Option #3: Both \(x = 3\) and \(x = 4\) are solutions.