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