Assertion (A): The discriminant of the quadratic equation $x^2 + 2\sqrt{2}x + 1 = 0$ is greater than zero.

Reason (R): If the discriminant of a quadratic equation is greater than zero, the quadratic equation has real and distinct roots.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Given,

$x^2 + 2\sqrt{2}x + 1 = 0$

Comparing $x^2 + 2\sqrt{2}x + 1 = 0$ with ax² + bx + c = 0 we get,

a = 1, b = $2\sqrt{2}$ and c = 1.

We know that,

Discriminant (D) = b² - 4ac = $(2\sqrt{2})^2$ - 4 × (1) × (1)

= 8 - 4 = 4; which is positive.

Since, D = 4 > 0, the discriminant is greater than zero.

So, Assertion (A) is true.

D > 0 Real and distinct roots

D = 0 Real and equal roots

D < 0 Imaginary roots

If Discriminant is grater than zero,

Real and distinct roots

So, Reason (R) is true.

Thus, Both A and R are true, but R is not the correct explanation of A.

Hence, option 2 is the correct option.