Find all zeros of the equation.

p (x) = x^3 - 4x^2+x+6

p (x) = x^3 - 4x^2+x+6 roots x = 3 or x = 2 or x = - 1

Step-by-step explanation:

Solve for x:

x^3 - 4 x^2 + x + 6 = 0

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

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

Split into three equations:

x - 3 = 0 or x - 2 = 0 or x + 1 = 0

Add 3 to both sides:

x = 3 or x - 2 = 0 or x + 1 = 0

Add 2 to both sides:

x = 3 or x = 2 or x + 1 = 0

Subtract 1 from both sides:

Answer: x = 3 or x = 2 or x = - 1