**Quadratic Equation and Its Roots:**

A quadratic equation is a polynomial equation of degree 2, which can be written in the form of ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

The roots of a quadratic equation are the values of x that satisfy the equation. These roots can be real or complex numbers, depending on the discriminant of the quadratic equation.

**Discriminant and Nature of Roots:**

The discriminant (D) of a quadratic equation is given by the expression D = b^2 - 4ac. It determines the nature of the roots of the quadratic equation.

1. If D > 0, then the quadratic equation has two distinct real roots.
2. If D = 0, then the quadratic equation has two equal real roots.
3. If D < 0,="" then="" the="" quadratic="" equation="" has="" two="" complex="" roots="" (conjugate="" />

**Reason: c * b^2 - 4ac > 0 for Two Distinct Real Roots:**

For the quadratic equation ax^2 + bx + c = 0 to have two distinct real roots, the discriminant (D) must be greater than 0.

Let's analyze the expression c * b^2 - 4ac:

1. If c * b^2 - 4ac > 0, it implies that D = c * b^2 - 4ac > 0.
2. Since D > 0, the quadratic equation has two distinct real roots.

Therefore, the reason c * b^2 - 4ac > 0 holds true for the quadratic equation to have two distinct real roots.

**Completing the Square Method:**

The method of completing the square is a technique used to solve quadratic equations. It involves manipulating the equation to express it in the form of a perfect square trinomial and then taking the square root of both sides to find the roots.

**Explanation:**

The statement that a quadratic equation can never be solved by using the method of completing the squares is incorrect. The method of completing the square is one of the methods used to solve quadratic equations.

The steps involved in solving a quadratic equation using the method of completing the squares are as follows:

1. Write the quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants.
2. Divide the equation by the coefficient of x^2, if necessary, to make the coefficient of x^2 equal to 1.
3. Move the constant term (c) to the other side of the equation.
4. Complete the square by adding the square of half the coefficient of x to both sides of the equation.
5. Express the left side of the equation as a perfect square trinomial.
6. Take the square root of both sides of the equation and solve for x.
7. Write down the two solutions obtained.

Therefore, the quadratic equation can indeed be solved by using the method of completing the squares.