Question

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

Answer 1

The coefficients are rational, the roots should be either rational or if irrational or complex, must occur in pairs with their conjugates.

∵1+2i,2−

3

and 5 are the three roots given.

The irrational root 2−

3

will have its conjugate 2+

3

a root as well.

Similarly, 1−2i is also a root.

∴ there exist at least 5 roots of f(x)=0 and hence least value of n is 5.

is the right answer and follow me