Question

Determine where the values 4 and 6 are solutions to the quadratic equation x2−10x+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

Only x=4 is a solution
Only x=4 is a solution

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

Both x=4 and x=6 are solutions

Answer 1

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 see if it equals zero.

**For \(x = 4\):**

\[
4^2 - 10(4) + 24 = 16 - 40 + 24 = 0
\]

So, \(x = 4\) is a solution.

**For \(x = 6\):**

\[
6^2 - 10(6) + 24 = 36 - 60 + 24 = 0
\]

So, \(x = 6\) is also a solution.

Since both \(x = 4\) and \(x = 6\) satisfy the equation \(x^2 - 10x + 24 = 0\), the correct answer is:

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