Determind the nature of the solutions of the equation x^2+4=0
Choose the nature of the solutions of the equation.
A) 2 imaginary solution
b) 1 real solution
c) 2 real solutions
Thank you for your help.
x^2=-4
x= +- 2sqrt(-1)
so two solutions, both...
To determine the nature of the solutions of the equation x^2 + 4 = 0, we need to solve the equation and see what type of solutions it has.
Step 1: Start with the equation x^2 + 4 = 0.
Step 2: Move the constant term to the other side of the equation, changing its sign:
x^2 = -4
Step 3: To eliminate the square term, take the square root of both sides of the equation:
√(x^2) = √(-4)
Step 4: The square root of -4 does not exist in the set of real numbers. However, we can express it as the product of the square root of -1 (i) and the square root of 4:
x = ± √(-1) * √(4)
Step 5: The square root of 4 is 2, so we have:
x = ± 2i, where i is the imaginary unit (√(-1))
Thus, the equation x^2 + 4 = 0 has 2 imaginary solutions.
Therefore, the correct answer is:
A) 2 imaginary solutions