Question

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Answer 1

Yes, consider the quadratic equation 2x² + x – 4 = 0 with rational coefficient.

The roots of the given quadratic equation are `(-1 + sqrt(33))/4` and `(-1 - sqrt(33))/4` are irrational.