If f(x) is a polynomial of degree n with rational coefficients and 1+2i,2−3 and 5 are three roots of f(x)=0 , then the least value of n is

α= 1+2i,β=1−2i, γ=2−3,δ=2+3and another root is 5.Number of roots are 5Degree n=5

α= 1+2i,β=1−2i, γ=2−3,δ=2+3and another root is 5.Number of roots are 5Degree n=5

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If $f (x)$ is a polynomial of degree $n$ with rational coefficients and $1 + 2 i, 2 - \sqrt{3}$ and 5 are three roots of $f (x) = 0$ , then the least value of n is

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$α = 1 + 2 i, β = 1 - 2 i, γ = 2 - \sqrt{3}, δ = 2 + \sqrt{3}$

and another root is 5.

Number of roots are 5

Degree $n = 5$

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