Suppose a polynomial function of deglee 5 with rational coefficients has the given numbers as zeros. Find the other zero(s).
1,2,1-4i, 5
Final Answer: The missing zero is \(\boxed{1+4i}\).
Step 1 :Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros: 1, 2, 1-4i, 5.
Step 2 :A polynomial function of degree 5 has 5 zeros.
Step 3 :If a complex number is a zero of a polynomial with real coefficients, then its conjugate is also a zero.
Step 4 :So, the missing zero is the conjugate of the given complex zero, which is 1+4i.
Step 5 :Final Answer: The missing zero is \(\boxed{1+4i}\).