Problem

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

Solution

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 \(\boxed{1+4i}\).

From Solvely APP
Source: https://solvelyapp.com/problems/c19ZfOuS5w/

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