Question

x^4-4x^3+x^2-4x

Answer 1

Solve for x over the real numbers:
x (-4+x-4 x^2+x^3) = 0
Solve each term in the product separately.
Split into two equations:
x = 0 or -4+x-4 x^2+x^3 = 0
Look at the second equation: Factor the left hand side.
The left hand side factors into a product with two terms:
x = 0 or (-4+x) (1+x^2) = 0
Solve each term in the product separately.
Split into two equations:
x = 0 or -4+x = 0 or 1+x^2 = 0
Look at the second equation: Solve for x.
Add 4 to both sides:
x = 0 or x = 4 or 1+x^2 = 0
Look at the third equation: Isolate terms with x to the left hand side.
Subtract 1 from both sides:
x = 0 or x = 4 or x^2 = -1
Show the equation has no solution.
x^2 = -1 has no solution since for all x on the real line, x^2 >=0 and -1ɘ:
Answer: |
| x = 0 or x = 4

Answer 2

Thank you!! really helped!