Solve the equation and express each solution in a+bi form. x^4-7x^2-8=0 a. x = -1, 1, 2 sqrt 2, or -2 sqrt 2 b. x = -i, i, 2 sqrt 2, or -2 sqrt 2 c. x = -1, 1, 2 sqrt 2i, or -2 sqrt 2i d. x = -i, i, 2 sqrt 2i, or -2 sqrt 2i

Because this is a fourth degree that will be tricky to factor as it is, we will do a u substitution. Let . We can now rewrite that polynomial in terms of u: . Filling into the quadratic formula we have . Simplifying down and or . That means that u = 8 or u = -1. But don't forget that we let , so we have to put x-squared back in for u. That gives us which simplifies down to . That also gives us . When we take the square root of -1, we have to use the fact that -1 = i^2, so we sub that in to get . All in all, your solutions are as follows: which is choice b.