To determine whether the values \( x = 3 \) and \( x = 4 \) are solutions to the quadratic equation \( x^2 - 7x + 12 = 0 \), we can substitute these values into the equation and check if the left side equals zero.
First, let's check \( x = 3 \):
\[ 3^2 - 7(3) + 12 = 9 - 21 + 12 = 9 - 21 + 12 = 0 \]
Since the left side equals zero, \( x = 3 \) is a solution.
Now let's check \( x = 4 \):
\[ 4^2 - 7(4) + 12 = 16 - 28 + 12 = 16 - 28 + 12 = 0 \]
Since the left side also equals zero, \( x = 4 \) is also a solution.
Both \( x = 3 \) and \( x = 4 \) are solutions to the equation.
Therefore, the correct answer is:
Option #3: Both \( x = 3 \) and \( x = 4 \) are solutions.