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

Question

Dr. Abubacker · Accepted Answer

(a)
Since, $(1 + 2i),\ (2 - \sqrt{3})$ and 5 are the some roots of polynomial $f(x)$ of degree $n$. As we know that conjugate are also the roots of the polynomial. Therefore, $(1 - 2i)$ and $(2 + \sqrt{3})$ are also the roots of the polynomial.
$	herefore$ The least value of $n$ is 5

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

Explanation

Reviewed by Dr. Abubacker

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