If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2 i, 2-\sqrt{3}$ and 5 are three…
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
$5$
$4$
$3$
$6$
Solution
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