Determine whether the values 4 and 6 are solutions to the quadratic equation: x^2 - 10x + 24

To determine if the values 4 and 6 are solutions to the quadratic equation \( x^2 - 10x + 24 = 0 \), we can substitute each value into the equation and check if it holds true (i.e., if the left-hand side equals zero).

1. **Checking \( x = 4 \)**:
\[
4^2 - 10(4) + 24 = 16 - 40 + 24
\]
\[
= 16 - 40 + 24 = 0
\]
Since the left-hand side equals 0, \( x = 4 \) is a solution to the equation.

2. **Checking \( x = 6 \)**:
\[
6^2 - 10(6) + 24 = 36 - 60 + 24
\]
\[
= 36 - 60 + 24 = 0
\]
Since the left-hand side also equals 0, \( x = 6 \) is a solution to the equation.

Thus, both values \( 4 \) and \( 6 \) are indeed solutions to the quadratic equation \( x^2 - 10x + 24 = 0 \).