6
QuizMultiple Choice

Solving Polynomial Equations with Complex Solutions — Quiz

Question 6 • Algebra 2 with Probability

What are the solutions to negative 24 x minus 24 is equal to x cubed plus 8 x squared ?

Answer
A
negative 2 comma negative 3 plus i square root of 3 comma negative 3 minus i square root of 3
B
negative 1 comma negative 3 plus i square root of 3 comma negative 3 minus i square root of 3
C
1 comma 3 plus i square root of 3 comma 3 minus i square root of 3
D
2 comma 3 plus i square root of 3 comma 3 minus i square root of 3

Explanation

Move all terms to one side: x³ + 8x² + 24x + 24 = 0. The roots in choice B give the factors (x + 2) and (x + 3 − i√3)(x + 3 + i√3) = x² + 6x + 12. Their product is x³ + 8x² + 24x + 24, so the solutions are −2, −3 + i√3, and −3 − i√3.

AI-written and checked against the verified answer.

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