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