Question

Determine whether the values 3 and 4 are solutions to the quadratic equation x^2 −7x+12=0
, 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 \( x = 3 \) and \( x = 4 \) are solutions to the quadratic equation \( x^2 - 7x + 12 = 0 \), we can substitute these values into the equation and check if the left side equals zero.

First, let's check \( x = 3 \):

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

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

Now let's check \( x = 4 \):

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

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

Both \( x = 3 \) and \( x = 4 \) are solutions to the equation.

Therefore, the correct answer is:

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