7
QuizMultiple Choice

Solving Polynomial Equations with Complex Solutions

Question 7 • FL-1200330-Algebra 2 CR

Consider the equation 4x4 – 8x3 + 4x2 – 128x – 960 = 0. The real solutions are 5 and –3. What are the nonreal solutions?

Answer
A
–2i, 2i
B
–4i, 4i
C
–8i, 8i
D
–16i, 16i

Explanation

Since 5 and −3 are roots, the polynomial has the factor (x − 5)(x + 3) = x² − 2x − 15. Dividing the polynomial by 4(x² − 2x − 15) leaves x² + 16, so the remaining equation is x² + 16 = 0. Thus x² = −16 and the nonreal solutions are −4i and 4i, choice B.

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