Question
Show how many solutions are in the solution set for the equation 3x2=21 .(1 point)
Responses
one
one
two
two
infinitely many
infinitely many
zero
Responses
one
one
two
two
infinitely many
infinitely many
zero
Answers
GPT-4o mini
To solve the equation \(3x^2 = 21\), we follow these steps:
1. Divide both sides by 3 to isolate \(x^2\):
\[
x^2 = 7
\]
2. Next, we take the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions:
\[
x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7}
\]
Thus, the equation \(3x^2 = 21\) has **two solutions**.
So the correct response is:
**two**.
1. Divide both sides by 3 to isolate \(x^2\):
\[
x^2 = 7
\]
2. Next, we take the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions:
\[
x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7}
\]
Thus, the equation \(3x^2 = 21\) has **two solutions**.
So the correct response is:
**two**.