Solve the equation x^5-4x^4+4x^3+2x^2-5x+2=0

x = 2 or x = 1 or x = - 1

Step-by-step explanation:

Solve for x over the real numbers:

x^5 - 4 x^4 + 4 x^3 + 2 x^2 - 5 x + 2 = 0

The left hand side factors into a product with three terms:

(x - 2) (x - 1) ^3 (x + 1) = 0

Split into three equations:

x - 2 = 0 or (x - 1) ^3 = 0 or x + 1 = 0

Add 2 to both sides:

x = 2 or (x - 1) ^3 = 0 or x + 1 = 0

Take cube roots of both sides:

x = 2 or x - 1 = 0 or x + 1 = 0

Add 1 to both sides:

x = 2 or x = 1 or x + 1 = 0

Subtract 1 from both sides:

Answer: x = 2 or x = 1 or x = - 1