SOLUTION: i need help with this question :Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. radical 2,5i thank

1. If the polynomial with rational coefficients has the root  ,  it also has the root .


2. If the polynomial with real coefficients has the root 5i, it also has the complex conjugated root  -5i.


3. So, your polynomial must have the roots ,  ,  5i  and  -5i.


4. If so, it must be divisible by the product  =  =  .


5. If you are looking for the polynomial of lowest degree with such properties,
   it is exactly THIS polynomial f(x) = .