If the discriminant of the quadratic equation, ax² + bx + c = 0, a ≠ 0 is greater than zero and a perfect square and a, b, c are rational, then the roots are:

1. rational and equal

2. irrational and unequal

3. irrational and equal

4. rational and unequal

If the discriminant of a quadratic equation, ax² + bx + c = 0, is greater than zero and a perfect square and b is irrational, then the roots are:

1. irrational and unequal

2. irrational and equal

3. rational and unequal

4. rational and equal

Which of the following is a quadratic equation?

1. x² + 1 = (2 - x)² + 3

2. 2x² + 3 = (5 + x)(2x - 3)

3. x³ - x² = (x - 1)³

4. none of these

Which of the following is not a quadratic equation?

1. 3x - x² = x² + 5

2. (x + 2)² = 2(x² - 5)

3. $(\sqrt{2}x + 3)^{2} = 2x^{2} + 6$

4. (x - 1)² = 3x² + x - 2