Is the textbook wrong?

[JackSonSmith]

-2-i is a solution of the equation z^4 - 5z^2 + 4z+30=0. Find the other solutions of the equation.

I"m getting z = 2+ root2 i , 2 - root 2 i , -2 - i and - 2 + i

However the textbook says that the answers are just z = 2+ root2 i , 2 - root 2 i , and - 2 + i

[cosine]

-2-i is a solution of the equation z^4 - 5z^2 + 4z+30=0. Find the other solutions of the equation.

I"m getting z = 2+ root2 i , 2 - root 2 i , -2 - i and - 2 + i

However the textbook says that the answers are just z = 2+ root2 i , 2 - root 2 i , and - 2 + i

Generally when the textbook gives you a solution of an existing function, they won't include that solution in the answers, as its already given. So, you are right, those four are the solutions. We know this also because the highest degree of z is 4, hence 4 solutions. AND, because our coefficients are real, the complex roots will occur in conjugate pairs, so if -2-i is a solution, so is it's conjugate -2 + i.


Hope it helped

[JackSonSmith]

Thank-you. That question had me wondering for a while.