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QuizMultiple Choice

Solving Polynomial Equations with Complex Solutions — Quiz

Question 1 • Algebra 2 with Probability

Consider the equation 4 x to the 4th power minus 8 x cubed plus 4 x squared minus 128 x minus 960 is equal to 0 The real solutions are 5 and negative 3 What are the nonreal solutions?

Answer
A
negative 2 i comma 2 i
B
negative 8 i comma 8 i
C
negative 16 i comma 16 i
D
negative 4 i comma 4 i

Explanation

The two real roots give the factor (x − 5)(x + 3) = x² − 2x − 15. Dividing the equation’s polynomial by this factor leaves 4(x² + 16) = 0. Thus x² = −16, so the nonreal solutions are −4i and 4i, matching choice D.

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