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
A. Only x=3 is a solution
B. Only x=4 is a solution
C. Both x = 3 and x = 4 are solutions
D. Neither x = 3 nor x = 4 is a solution

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 and check if it holds true (i.e., equals zero).

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

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

Since both values satisfy the equation, we conclude that:

**C. Both x = 3 and x = 4 are solutions**.