Question

Solve the Equation x^5-5x^3+4x=0

a) 0, (-/+)1, (-/+)3
b) 0, (-/+)2, (-/+)3
c) 0, (-/+)1, (-/+)2
d) 0, (-/+)2, (-/+)4

Answer 1

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

Explanation:

Solve for x:

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

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

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

Split into five equations:

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

Add 2 to both sides:

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

Add 1 to both sides:

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

Subtract 1 from both sides:

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

Subtract 2 from both sides:

Answer: x = 2 or x = 1 or x = 0 or x = -1 or x = -2