Question

Question

How many solutions are in the solution set for each quadratic equation below?(3 points)
5x2=50
This quadratic equation would have
solution(s).

3x2=−12
This quadratic equation would have
solution(s).

8x2=0
This quadratic equation would have
solution(s).

Answer 1

To determine the number of solutions for each quadratic equation, we can rewrite them in the standard form \(ax^2 + bx + c = 0\) and consider their discriminants.

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

   • Rearranging gives: \(5x^2 - 50 = 0\)
   • Dividing by 5: \(x^2 - 10 = 0\)
   • This can be written as \(x^2 = 10\).
   • The solutions are \(x = \pm \sqrt{10}\), which means there are 2 solutions.

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

   • Rearranging gives: \(3x^2 + 12 = 0\)
   • Dividing by 3: \(x^2 + 4 = 0\)
   • We write \(x^2 = -4\).
   • Since the square of a real number cannot be negative, there are 0 solutions in the real number system (the solutions are complex).

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

   • Rearranging gives: \(8x^2 = 0\)
   • Dividing by 8: \(x^2 = 0\).
   • The only solution is \(x = 0\), which means there is 1 solution.

Summary:

• 5x² = 50: 2 solutions
• 3x² = -12: 0 solutions
• 8x² = 0: 1 solution