Determine whether the values 3 and 4 are solutions to the quadratic equation x2−7x+12=0

Question

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

Option #1: Only x=3
is a solution.

Option #2: Only x=4
is a solution.

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

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

(1 point)

Answer 1

To determine whether 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 it holds true.

1. Testing \(x = 3\): \[ 3^2 - 7(3) + 12 = 9 - 21 + 12 = 9 - 21 + 12 = 0 \] So \(x = 3\) is a solution.

2. Testing \(x = 4\): \[ 4^2 - 7(4) + 12 = 16 - 28 + 12 = 16 - 28 + 12 = 0 \] So \(x = 4\) is also a solution.

Since both values satisfy the equation, the correct answer is:

Option #3: Both \(x = 3\) and \(x = 4\) are solutions.