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)
Option #

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. Substituting \( x = 3 \): \[ (3)^2 - 7(3) + 12 = 9 - 21 + 12 = 0 \] This checks out, so \( x = 3 \) is a solution.

2. Substituting \( x = 4 \): \[ (4)^2 - 7(4) + 12 = 16 - 28 + 12 = 0 \] This also checks out, so \( x = 4 \) is a solution.

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

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