Solution Sets of Quadratic Equations Practice

Question

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Question
Determine whether the values 3 and 4 are solutions to the quadratic equation x2−7x+12=0
x
2
−
7
x
+
12
=
0
, and then select the correct answer from the following options.

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

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

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

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

(1 point)

Answer 1

To determine whether the values \( x = 3 \) and \( x = 4 \) are solutions to the quadratic equation \( x^2 - 7x + 12 = 0 \), we will substitute both values into the equation and check if the equation equals zero.

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

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

Since both values satisfy the equation \( x^2 - 7x + 12 = 0 \), the correct answer is:

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