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 roots of the equation px² + qx + r = 0, where p ≠ 0, are given by:

1. $x = \dfrac{-p \pm \sqrt{q^{2} - 4pr}}{2p}$

2. $x = \dfrac{-q \pm \sqrt{q^{2} - 2pr}}{4p}$

3. $x = \dfrac{-q \pm \sqrt{q^{2} - 4pr}}{2p}$

4. $x = \dfrac{-q \pm \sqrt{q^{2} - 4pr}}{2q}$

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