<s>[INST] Equation $3x^4 + 2x^3 + 9x^2 + 4x + 6 = 0$ Solve the equation 
$$3x^4 + 2x^3 + 9x^2 + 4x + 6 = 0$$
Having a complex root of modulus $1$.
To get the solution, I tried to take a complex root $\sqrt{\frac{1}{2}} + i \sqrt{\frac{1}{2}}$ but couldn't get the solution right. Please help me.
 [/INST] HINT:
$$3x^4 + 2x^3 + 9x^2 + 4x + 6 = (x^2 + 2)(3x^2 + 2x + 3)$$
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