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
The equation 3x^2 = 21 can be rewritten as x^2 = 7.
The equation is a quadratic equation, which can have at most two solutions.
Therefore, the solution set for the equation has two solutions.
To determine the number of solutions in the solution set for the equation 3x^2 = 21, we can start by rewriting the equation as a quadratic equation in standard form:
3x^2 - 21 = 0
Next, we can factor out the common factor of 3:
3(x^2 - 7) = 0
Now, we can set each factor equal to zero and solve for x:
1) x^2 - 7 = 0
To solve this quadratic equation, we can use the square root property. Taking the square root of both sides gives:
x^2 = 7
x = ±√7
Therefore, for the first factor, we have two solutions: x = √7 and x = -√7.
2) 3 = 0
However, the equation 3 = 0 is a contradiction. Therefore, it has no solutions.
In summary, the equation 3x^2 = 21 has two solutions (x = √7 and x = -√7) and zero solutions (3 = 0) simultaneously.
To determine the number of solutions in the solution set for the given equation, we need to solve the equation and find the values of x that satisfy it.
The given equation is 3x^2 = 21.
To solve this equation, we need to isolate the variable x.
First, divide both sides of the equation by 3 to get: x^2 = 7.
Taking the square root of both sides to eliminate the exponent, we have two possible solutions for x: x = √7 and x = -√7.
Therefore, the solution set for the equation 3x^2 = 21 has two solutions, which are x = √7 and x = -√7.