Question 1027286
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 you!
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1. If the polynomial with rational coefficients has the root  {{{sqrt(2)}}},  it also has the root {{{-sqrt(2)}}}.


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 {{{sqrt(2)}}},  {{{-sqrt(2)}}},  5i  and  -5i.


4. If so, it must be divisible by the product {{{(x-sqrt(2))*(x-(-sqrt(2)))*(x-5i)*(x-(-5i))}}} = {{{(x-sqrt(2))*(x+sqrt(2))*(x-5i)*(x+5i))}}} = {{{(x^2 -2)*(x^2 + 25)}}} .


5. If you are looking for the polynomial of lowest degree with such properties,
   it is exactly THIS polynomial f(x) = {{{(x^2 -2)*(x^2 + 25)}}}.
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