Question

Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

Answer 1

Yes, consider the quadratic equation with all distinct irrationals coefficients

i.e., `sqrt(3)x^2 - 7sqrt(3)x + 12sqrt(3)` = 0.

The roots of this quadratic equation are 3 and 4

Which are rationals.