x4-2x3+x2=0

Solve x^4 − 2x^3 + x^2 = 0.

• Factor: x^2(x^2 − 2x + 1) = x^2(x − 1)^2 = 0
• So x^2 = 0 ⇒ x = 0
• And (x − 1)^2 = 0 ⇒ x = 1

Solutions: x = 0 or x = 1 (each with multiplicity 2).