Question

One of the roots of the equation \((x+1)^4 + 81 = 0\) is

• A. \(3(\frac{1+i}{\sqrt{2}})\)
• B. \(\frac{-3+\sqrt{2}+3i}{\sqrt{2}}\)
• C. \(-(\frac{3+\sqrt{2}+i}{\sqrt{2}})\)
• D. \(-(\frac{3+3i}{\sqrt{2}})\)

Hint:

When the roots you calculate for a polynomial equation don't match any of the given options, double-check the problem statement for simple sign errors. A common typo is having `(x+a)` when `(x-a)` was intended, or vice-versa. Testing the modified equation can quickly lead to the correct option.

Answer 1

The Correct Option is B