Evaluating the Roots

Question

Suppose f(x)=x^4(6−8x^9).

1) The roots are ?

2) As x→∞, f(x)→ ?

3) As x→ −∞, f(x)→ ?

Answer 1

x=0 is a root of f(x) with a multiplicity of 4

9 more roots by setting (6-8x⁹)=0

z=(3/4+0i)^(1/9) has one real root, and 8 complex roots.

x₁=(3/4)^(1/9) where xis real number

z_k+1=(3/4)^(1/9)(cos(2πk/9)+isin(2πk/9)),,,,,,,,k=1 to 8

Answer 2

1) The roots are ?

2) As x→∞, f(x)→ - infty

3) As x→ −∞, f(x)→ infty