f(x) is a polynomial with rational coefficients and given roots of f(x) are 1+2i,2−√3,5. ∵ One root is imaginary and one root is irrational. ⇒ Other two roots are (1−2i) and (2+√3). ∴ Roots of f(x) are 1+2i,1−2i,2−√3,2+√3,5. Number of roots =5 Degree of polynomial =5