If (x) is a polynomal of degree n with rational coeficients and 1 + `2i, 2 - sqrt(3)` and 5 are three roots of f(x) = 0 , then the least value of n is

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

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

The equation of lowest degree with rational coeficients having a root sqrt(3) + sqrt(2)i is

The equation of lowest degree with rational coeficients having a root sqrt(3) + sqrt(2)i is

The equation of lowest degree with rational coeficients having a root - sqrt(2) - sqrt(2)i is

LetP(x)=0 be the polynomial equation of least possible degree with rational coefficients having 3sqrt7+3sqrt49 as a root. Then the product of all the roots of P(x)=0 is

For a prime positive integer n,3sqrt(n)+3sqrt(n^(2)) is a root of a polynomial with rational coefficients and least possible degree.The products of all roots of equation is

Let p (x) be a polynomial equation of least possible degree, with rational coefficients, having ""^(3)sqrt7 +""^(3)sqrt49 as one of its roots. Then the product of all the roots of p (x) =0 is: