Question

Find a polynomial function p of lowest​ degree, having rational​ coefficients, with the given zero. 5i

Answer 1

If we have one zero of +5i, we also have to have its conjugate which is -5i.  Therefore, the factors that we will FOIL to get that polynomial are (x+5i)(x-5i).  That distribution results in $x^{2} -25 i^{2}$.  I'm sure by now you know that i squared is equal to -1, so -25(-1) = 25.  So our polynomial is $x^{2} +25=y$