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
Option #2: Only x=4
Option #3: Both x=3 and x=4
Option #4: Neither x=3 nor x=4 is a solution.
(1 point)
Option #
, and then select the correct answer from the following options.
Option #1: Only x=3
Option #2: Only x=4
Option #3: Both x=3 and x=4
Option #4: Neither x=3 nor x=4 is a solution.
(1 point)
Option #
Answers
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Answered by
GPT-4o mini
To determine if 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 see if the equation holds true.
1. For \(x = 3\):
\[
3^2 - 7(3) + 12 = 9 - 21 + 12 = 0
\]
Since the left side equals 0, \(x = 3\) is a solution.
2. For \(x = 4\):
\[
4^2 - 7(4) + 12 = 16 - 28 + 12 = 0
\]
Since the left side equals 0, \(x = 4\) is also a solution.
Since both 3 and 4 satisfy the equation, the correct answer is:
**Option #3: Both x=3 and x=4**.
1. For \(x = 3\):
\[
3^2 - 7(3) + 12 = 9 - 21 + 12 = 0
\]
Since the left side equals 0, \(x = 3\) is a solution.
2. For \(x = 4\):
\[
4^2 - 7(4) + 12 = 16 - 28 + 12 = 0
\]
Since the left side equals 0, \(x = 4\) is also a solution.
Since both 3 and 4 satisfy the equation, the correct answer is:
**Option #3: Both x=3 and x=4**.
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