Question
Find the root(s) of the equation = 121.
Responses
A x = x = √11
B x = ±x = ± √11
C x = 11
D x = +11
Responses
A x = x = √11
B x = ±x = ± √11
C x = 11
D x = +11
Answers
GPT-4o mini
To find the root(s) of the equation \( x^2 = 121 \), we can take the square root of both sides.
\[
x = \pm\sqrt{121}
\]
Since the square root of 121 is 11, we have:
\[
x = \pm 11
\]
This means that the solutions are \( x = 11 \) and \( x = -11 \).
Looking at the options given:
A. \( x = \sqrt{11} \) - Incorrect
B. \( x = \pm \sqrt{11} \) - Incorrect
C. \( x = 11 \) - Correct, but only one root
D. \( x = +11 \) - Correct, but only one root
The most accurate representation of the solution \( x = \pm 11 \) is not directly in the options.
So the best answer choice that represents part of the solution is:
**C.** \( x = 11 \) (although it does not account for the negative root).
If there is a need to include both roots, option B represents the structure of including both roots, but it's incorrect in the context of the roots of 121.
\[
x = \pm\sqrt{121}
\]
Since the square root of 121 is 11, we have:
\[
x = \pm 11
\]
This means that the solutions are \( x = 11 \) and \( x = -11 \).
Looking at the options given:
A. \( x = \sqrt{11} \) - Incorrect
B. \( x = \pm \sqrt{11} \) - Incorrect
C. \( x = 11 \) - Correct, but only one root
D. \( x = +11 \) - Correct, but only one root
The most accurate representation of the solution \( x = \pm 11 \) is not directly in the options.
So the best answer choice that represents part of the solution is:
**C.** \( x = 11 \) (although it does not account for the negative root).
If there is a need to include both roots, option B represents the structure of including both roots, but it's incorrect in the context of the roots of 121.