If a, b, c ∈ R, show that the roots of the equation (a - b)x² + (b + c - a)x - c = 0 are rational.

If a, b, c are rational, prove that the roots of the equation (b - c)x² + (c - a)x + (a - b) = 0 are also rational.

The discriminant of the quadratic equation ax² + bx + c = 0, a ≠ 0 is given by:

1. b² - 2ac

2. b² - ac

3. b² - 4ac

4. none of these