how to you use the irrational conjugate theorum

Question

how to you use the irrational conjugate theorumTo find the polynomial function of least degree

Answer 1

If you know one imaginary zero, then the conjugate is necessarily another imaginary zero

IF i is a zero so is -i.

IF 1-i is a zero so is 1+i

if i is a zero then a factor of the polynomial is (x^2+1) = (x-i)(x+i) take each zero change the sign and stick an x in front of it to get the factor of the polynomial

Answer 2

For each given irrational solution, the conjugate mate must also be a solution.

The same is true for imaginary/complex solutions, which also must be rationalized.

Ex.

x = 3, -1, 2 + rad3, 5 - 2i are the given solutions...

Then 2 - rad3 and 5 + 2i MUST also be solutions

Therefore, there are SIX (6) solutions, which makes it a 6th degree polynomial.