Which of the following is a root of the polynomial function F (x) = x^4+2x^3-3x^2-6x?

Answer: x = 0, √3, - √3, - 2

Step-by-step explanation:

x⁴ + 2x³ - 3x² - 6x

= x (x³ + 2x² - 3x - 6)

= ↓ x² (x + 2) - 3 (x + 2)

= x (x² - 3) (x + 2)

= x (x - √3) (x + √3) (x + 2)

Set each factor equal to zero to find the roots:

x = 0 x - √3 = 0 x + √3 = 0 x + 2 = 0

x = √3 x = - √3 x = - 2