Determine whether the values 3 and 4 are solutions to the quadratic equation x^2−7x+12=0

Question

, and then select the correct answer from the following options.

Option #1: Only x=3

Option #2: Only x=4

Option #3: Both x=3 and x=4
Option #4: Neither x=3 nor x=4 is a solution.

(1 point)
Option #

Answer 1

To determine if the values 3 and 4 are solutions to the quadratic equation \(x^2 - 7x + 12 = 0\), we can substitute each value into the equation and see if the equation holds true.

1. For \(x = 3\):

\[ 3^2 - 7(3) + 12 = 9 - 21 + 12 = 0 \]

Since the left side equals 0, \(x = 3\) is a solution.

2. For \(x = 4\):

\[ 4^2 - 7(4) + 12 = 16 - 28 + 12 = 0 \]

Since the left side equals 0, \(x = 4\) is also a solution.

Since both 3 and 4 satisfy the equation, the correct answer is:

Option #3: Both x=3 and x=4.