Question
Solution Sets of Quadratic Equations Quick Check
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Question
Show how many solutions are in the solution set for the equation 3x2=21.(1 point)
Responses
one
one
infinitely many
infinitely many
two
two
zero
zero
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Answers
GPT-4o mini
To determine how many solutions the equation \(3x^2 = 21\) has, we can start by rewriting the equation in standard form.
1. Divide both sides by 3:
\[
x^2 = 7
\]
2. Now, we can solve for \(x\) by taking the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions: \(x = \sqrt{7}\) and \(x = -\sqrt{7}\).
Therefore, the equation \(3x^2 = 21\) has **two** solutions.
The correct response is:
**two**
1. Divide both sides by 3:
\[
x^2 = 7
\]
2. Now, we can solve for \(x\) by taking the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions: \(x = \sqrt{7}\) and \(x = -\sqrt{7}\).
Therefore, the equation \(3x^2 = 21\) has **two** solutions.
The correct response is:
**two**