Given the equation $4x^5 + 3x^4 + 2x^3 + x^2 + x - 11 = 0$, how do I find all complex roots? Fundamental theorem of algebra states that since this is a 5th degree polynomial, there are $5$ roots. I have used rational factor theorem to find that $(x-1)$ is a factor but this leaves me with $(x-1)(4x^4 + 7x^3 + 9x^2 + 10x + 11)$ and the quartic function has no real roots and is not factorable. How do I find the four imaginary roots for that particular quartic?



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