Find all the zeros of each equation

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

you would get the answer of 1, i√5,-i√5

x = 1 or x = i sqrt (5) or x = - i sqrt (5)

Step-by-step explanation:

Solve for x:

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

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

(x - 1) (x^2 + 5) = 0

Split into two equations:

x - 1 = 0 or x^2 + 5 = 0

Add 1 to both sides:

x = 1 or x^2 + 5 = 0

Subtract 5 from both sides:

x = 1 or x^2 = - 5

Take the square root of both sides:

Answer: x = 1 or x = i sqrt (5) or x = - i sqrt (5)