Question

Determine where the values 4 and 6 are solutions to the quadratic equation x^2 − 10x + 24
, and then select the correct answer from the following options.(1 point)
Responses

Only x=6 is a solution
Only x=6 is a solution

Both x=4 and x=6 are solutions
Both x=4 and x=6 are solutions

Neither x=4 nor x=6 is a solution.
Neither x=4 nor x=6 is a solution.

Only x=4 is a solution

Answer 1

To determine if \( x = 4 \) and \( x = 6 \) are solutions to the quadratic equation \( x^2 - 10x + 24 = 0 \), we need to substitute these values into the equation and see if either results in a true statement.

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

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

Since both \( x = 4 \) and \( x = 6 \) satisfy the equation, the correct answer is:

**Both x = 4 and x = 6 are solutions.**