Quadratic equation with complex coefficients

Introduction and State Quadratic Equation with real coefficients

A quadratic equation with rational coefficients can have

The quadratic equation with rational coefficients whose one root is 2-sqrt(3) is

Statement -1 : There is just one quadratic equation with real coefficient one of whose roots is 1/(sqrt2 +1) and Statement -2 : In a quadratic equation with rational coefficients the irrational roots are in conjugate pairs.

Statement -1 : There is just on quadratic equation with real coefficients, one of whose roots is 1/(3+sqrt7) and Statement -2 : In a quadratic equation with rational coefficients the irrational roots occur in pair.

Find the quadratic equation with rational coefficients whose one root is 1/(2+sqrt(5))

If 1+sqrt(2) is a root of a quadratic equation with rational coefficients,write its other root.

The quadratic equation with real coefficients has one root 2i^(*)s