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 Both x=4 and x=6 are solutions Both x=4 and x=6 are solutions Neither x4 nor x=6 is a solution. Neither x=4 nor x=6 is a solution. Only x=6 is a solution Only x=6 is a solution Only x=4 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 can substitute these values into the equation and check if they satisfy it.

1. For \( x = 4 \): \[ x^2 - 10x + 24 = 4^2 - 10(4) + 24 \] \[ = 16 - 40 + 24 \] \[ = 16 - 40 + 24 = 0 \] So, \( x = 4 \) is a solution.

2. For \( x = 6 \): \[ x^2 - 10x + 24 = 6^2 - 10(6) + 24 \] \[ = 36 - 60 + 24 \] \[ = 36 - 60 + 24 = 0 \] So, \( x = 6 \) is a solution.

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

Both x=4 and x=6 are solutions.