Suppose a polynomial function of degree 4 with rational coef

Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros Find the other zeros 1 + 2. 4 + squareroot 3 The other zeros are (Use a comma to separate answers)

Solution

solution

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if a+ib is a root of the function then there exist is another root a-ib and

if a+sqt(b) is a root of the function then there exist is another root a-sqrt(b)

here for the given polynomial 1+2i,4+sqrt(3) are two zeros

therefore the other zeros are 1-2i,4-sqrt(3)