Determine whether the values 3 and 4 are solutions to the quadratic equation x2−7x+12=0 , and then select the correct answer from the following options.

Question

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

1. For \( x = 3 \): \[ (3)^2 - 7(3) + 12 = 9 - 21 + 12 = 0 \] Since the equation is satisfied, \( x = 3 \) is a solution.

2. For \( x = 4 \): \[ (4)^2 - 7(4) + 12 = 16 - 28 + 12 = 0 \] Since the equation is also satisfied, \( x = 4 \) is also a solution.

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

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