Question 1105250
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{{{f(x) = (x-5)(x+3)^2}}}; its zeros are 5 and -3.<br>
If g(x) is a polynomial of degree 4 with the same real zeros as f(x) and with at least one imaginary root, then it must have single real zeros of 5 and -3 and one pair of imaginary zeros.<br>
With only those restrictions, a possible polynomial g(x) is
{{{g(x) = (x-5)(x+3)(x^2+1) = x^4-2x^3+16x^2-2x+15}}}