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
