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

If 1+2i is root of f(x) then1−2i is also rootIf 2−3 is root of f(x) then 2+3 is also root∴ The roots of f(x) are 1± 2i, 2±3 , 5∴ n=5

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

If 1+2i is root of f(x) then1−2i is also rootIf 2−3 is root of f(x) then 2+3 is also root∴ The roots of f(x) are 1± 2i, 2±3 , 5∴ n=5

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

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Detailed Solution

$\begin{array}{l} I f 1 + 2 i i s r o o t o f f (x) t h e n \\ 1 - 2 i i s a l s o r o o t \\ I f 2 - \sqrt{3} i s r o o t o f f (x) t h e n 2 + \sqrt{3} i s a l s o r o o t \\ ∴ T h e r o o t s o f f (x) a r e 1 \pm 2 i, 2 \pm \sqrt{3}, 5 \\ ∴ n = 5 \end{array}$