Show how many solutions are in the solution set for the equation 3x2=21 .(1 point)

Responses

one
one

zero
zero

two
two

infinitely many

1 answer

To determine how many solutions are in the solution set for the equation \(3x^2 = 21\), let's solve the equation.

First, divide both sides of the equation by 3 to isolate \(x^2\):

\(3x^2 = 21\)

\(x^2 = 7\)

Next, take the square root of both sides to solve for x. Remember, there are two square roots for any positive number, a positive and a negative root:

\(\sqrt{x^2} = \sqrt{7}\)

\(x = \pm\sqrt{7}\)

This gives us two solutions for x: \(x = \sqrt{7}\) and \(x = -\sqrt{7}\).

Therefore, the solution set contains two solutions.