How many solutions are in the solution set for each quadratic equation below?

Question

5x^2 = 50
3x^2 = -12
8x^2 = 0

Answer 1

To determine the number of solutions for each quadratic equation, we can analyze them one by one.

1. For the equation \( 5x^2 = 50 \):

   • First, divide both sides by 5: \[ x^2 = 10 \]
   • Since 10 is positive, we can take the square root: \[ x = \sqrt{10} \quad \text{or} \quad x = -\sqrt{10} \]
   • This equation has 2 solutions.

2. For the equation \( 3x^2 = -12 \):

   • Divide both sides by 3: \[ x^2 = -4 \]
   • Since -4 is negative, there are no real solutions (but there are complex solutions): \[ x = 2i \quad \text{or} \quad x = -2i \]
   • This equation has 0 real solutions (but 2 complex solutions).

3. For the equation \( 8x^2 = 0 \):

   • Divide both sides by 8: \[ x^2 = 0 \]
   • The only solution is: \[ x = 0 \]
   • This equation has 1 solution.

In summary:

• The first equation has 2 solutions.
• The second equation has 0 real solutions.
• The third equation has 1 solution.