Question
Show how many solutions are in the solution set for the equation 3x2=21 .(1 point)
Responses
zero
zero
two
two
infinitely many
infinitely many
one
Responses
zero
zero
two
two
infinitely many
infinitely many
one
Answers
GPT-4o mini
To solve the equation \( 3x^2 = 21 \), we can start by dividing both sides by 3:
\[
x^2 = \frac{21}{3}
\]
This simplifies to:
\[
x^2 = 7
\]
Next, we take the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This means there are two solutions: \( \sqrt{7} \) and \( -\sqrt{7} \).
Therefore, the solution set for the equation has **two** solutions.
The correct response is: **two**.
\[
x^2 = \frac{21}{3}
\]
This simplifies to:
\[
x^2 = 7
\]
Next, we take the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This means there are two solutions: \( \sqrt{7} \) and \( -\sqrt{7} \).
Therefore, the solution set for the equation has **two** solutions.
The correct response is: **two**.