Question

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

Answer 1

Answer: x = 0, √3, -√3, -2

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