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

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

The correct answer would be D.

Step-by-step explanation:

I took the test and got it correct!

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