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

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.

AI-written and checked against the verified answer.