Find all solutions to the equation x cubed minus 4 x squared plus 9 x minus 10 is equal to 0

Test the real roots suggested by the choices in the polynomial. Substituting x = 2 gives 8 − 16 + 18 − 10 = 0, so (x − 2) is a factor. Dividing x³ − 4x² + 9x − 10 by (x − 2) gives x² − 2x + 5, whose roots are x = (2 ± √(4 − 20))/2 = 1 ± 2i. The solutions are 2, 1 + 2i, and 1 − 2i, which is choice C.

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