Answer:
x=-1, x=3 e x=2i, x=-2i
Explanation:
Solve for x over the real numbers:
x^4 - 2 x^3 + x^2 - 8 x - 12 = 0
The left hand side factors into a product with three terms:
(x - 3) (x + 1) (x^2 + 4) = 0
Split into three equations:
x - 3 = 0 or x + 1 = 0 or x^2 + 4 = 0
Add 3 to both sides:
x = 3 or x + 1 = 0 or x^2 + 4 = 0
Subtract 1 from both sides:
x = 3 or x = -1 or x^2 + 4 = 0
Subtract 4 from both sides:
x = 3 or x = -1 or x^2 = -4
x^2 = -4 has no solution since for all x on the real line, x^2 >=0 and -4<0:
Answer: |
| x = 3 or x = -1