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 - $2\sqrt{x}$ + 7 = 0

2. 2x² - 5x = (x - 1)²

3. $x - \dfrac{1}{x} = 2x^{2}$

4. x² + $\dfrac{1}{x^{2}}$ = 2

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

The roots of the quadratic equation 2x² - x - 6 = 0 are:

1. -2, $\dfrac{3}{2}$

2. 2, $\dfrac{-3}{2}$

3. -2, $\dfrac{-3}{2}$

4. 2, $\dfrac{3}{2}$