What are the real and complex solutions of the polynomial equation?
0 = x^4 + 3x^2 – 4
A. –1, 1
B. 1, 2i
C. –1, 1, –2, 2
D. –1, 1, –2i, 2i
To find the real and complex solutions of the polynomial equation, we need to determine the values of x that make the equation equal to zero.
0 = x^4 + 3x^2 - 4
We can rewrite this equation as:
0 = (x^2 + 4)(x^2 - 1)
Setting each factor equal to zero and solving for x, we have:
x^2 + 4 = 0
x^2 = -4
x = ±√(-4) = ±2i
x^2 - 1 = 0
x^2 = 1
x = ±√(1) = ±1
Therefore, the real solutions are x = -1 and x = 1, and the complex solutions are x = -2i and x = 2i.
The correct answer is D: –1, 1, –2i, 2i.