Answer:
see below
Step-by-step explanation:
The four solutions are all complex.
The equation can be written in vertex form as ...
(x^2 -√3)^2 +1 = 0
This has solutions ...
x^2 -√3 = ±√-1 . . . . . . . . . . . . . . subtract 1, take the square root
x² = √3 ± i = 2∠±30° . . . . . . . . write in polar form to simplify root taking*
This has solutions for x ...
x = ±√(2∠±30°) = (±√2)∠±15° . . . . in polar form
x = ±√2(cos(15°) ± i·sin(15°)) . . . . . two conjugate pairs of solutions, total
x ≈ ±1.3660254 ±0.3660254i
_____
* We prefer not to have a complex number under a radical, as in ...
[tex]x=\pm\sqrt{\sqrt{3}\pm i}[/tex]
