Introduction and State Quadratic Equation with real coefficients

Quadratic equation with complex coefficients

A quadratic equation with rational coefficients can have

One of the roots of a quadratic equation with real coefficients is (1)/((2-3i)) . Which of the following implications is/are true? 1. The second root of the equation will be (1)/((3-2i)) . 2. The equation has no real root. 3. The equation is 13x^(2)-4x+1=0. Which of the above is/are correct ?

Find the quadratic equation with real coefficients which has (-5-i) as a root

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.

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.

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.

Find the quadratic equation with real coefficients which has 2+i as a root (i=sqrt-1) .

Find the quadratic equation with real coefficients which has 2±3i as a root (i=sqrt-1)