SOLUTION: A polynomial of lowest degree with rational coefficients which has 2, 3^1/2, 2i and 3i as zeroes would be of what degree?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A polynomial of lowest degree with rational coefficients which has 2, 3^1/2, 2i and 3i as zeroes would be of what degree?      Log On


   

Question 222446: A polynomial of lowest degree with rational coefficients which has 2, 3^1/2, 2i and 3i as zeroes would be of what degree?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, all complex zeros come in conjugate pairs. So there's another zero -2i as well (since -2i is the complex conjugate of 2i).

So there are 4 zeros: 2, sqrt%283%29, 2i, and -2i

By the fundamental theorem of algebra, this means that there is a polynomial of degree 4 that has these 4 zeros. So this means that the smallest degree is 4.