Question

Which description matches the solution to this equation: x^4- 81 = 0
A. all four solutions are real
B. two solutions are real; two are imaginary
C. all four solutions are imaginary
D. three solutions are real; one solution is imaginary

Answer 1

Two are real, two are imaginary.

\[x^4-81=0 \rightarrow x^4=81 \rightarrow x^2=\pm 9 \rightarrow x=\pm 3, \pm 3i\]