Question
Show how many solutions are in the solution set for the equation $3x^{2}=21$
one
zero
two
infinitely many
one
zero
two
infinitely many
Answers
GPT-4o mini
To determine the number of solutions for the equation \( 3x^2 = 21 \), we first simplify the equation by dividing both sides by 3:
\[
x^2 = \frac{21}{3}
\]
Calculating the right side gives:
\[
x^2 = 7
\]
Next, we solve for \( x \) by taking the square root of both sides. Remember that when taking the square root, we consider both the positive and negative roots:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions:
\[
x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7}
\]
Thus, we conclude that the equation \( 3x^2 = 21 \) has two distinct solutions.
The answer is:
\[
\boxed{two}
\]
\[
x^2 = \frac{21}{3}
\]
Calculating the right side gives:
\[
x^2 = 7
\]
Next, we solve for \( x \) by taking the square root of both sides. Remember that when taking the square root, we consider both the positive and negative roots:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions:
\[
x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7}
\]
Thus, we conclude that the equation \( 3x^2 = 21 \) has two distinct solutions.
The answer is:
\[
\boxed{two}
\]