Which of the following equations has two real and distinct roots ?

1. 2x² - $3\sqrt{2}x + \dfrac{9}{4}$ = 0

2. x² + x - 5 = 0

3. x² + 3x + $2\sqrt{2}$ = 0

4. 7x² - 3x + 1 = 0

For an equation having real and distinct roots :

b² - 4ac > 0

Comparing equation (1) with ax² + bx + c, we get :

a = 2, b = $-3\sqrt{2} \text{ and c } = \dfrac{9}{4}$

Substituting values in b² - 4ac,

⇒ $(-3\sqrt{2})^2 - 4 \times 2 \times \dfrac{9}{4}$

⇒ $18 - 18$

⇒ 0.

Comparing equation (2) with ax² + bx + c, we get :

a = 1, b = 1 and c = -5.

Substituting values in b² - 4ac,

⇒ 1² - 4 × 1 × (-5)

⇒ 1 + 20

⇒ 21.

Since, b² - 4ac > 21.

∴ x² + x - 5 = 0 has real and distinct roots.

Hence, Option 2 is the correct option.