The real root of the equation x cubed plus 10 x squared plus 29 x plus 30 is equal to 0 is negative 6 What are the nonreal solutions?

Since −6 is a root, divide x³ + 10x² + 29x + 30 by (x + 6). The quotient is x² + 4x + 5, so the remaining solutions satisfy x² + 4x + 5 = 0. Using the quadratic formula gives x = (−4 ± √(16 − 20))/2 = −2 ± i, which matches negative 2 plus or minus i.

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