Q58 / 160 · TS EAMCET 2004 · Mathematics

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

  • Correct answer
    A
    $5$
  • B
    $4$
  • C
    $3$
  • D
    $6$

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 .

Hence, the correct answer is option: 'A'.

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