**Quadratic Equation and its Roots:**

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The solutions to this equation are called the roots of the quadratic equation.

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

**Given Information:**

In the given quadratic equation, x^2 - 12x + a = 0, one root is thrice the other. Let's assume the roots of the equation are p and 3p, where p is a constant.

**Sum and Product of Roots:**

The sum of the roots of a quadratic equation is given by the formula: sum = -b/a.

The product of the roots of a quadratic equation is given by the formula: product = c/a.

**Applying the Given Information:**

We know that one root is p and the other root is 3p. Therefore, the sum of the roots is p + 3p = 4p.

By comparing this with the formula for the sum of roots, we have: 4p = -(-12)/1 = 12.

Simplifying, we find: p = 12/4 = 3.

Therefore, the roots of the quadratic equation are p = 3 and 3p = 9.

**Finding the Value of a:**

To find the value of a, we can use the product of roots formula.

The product of the roots is p * 3p = 3 * 9 = 27.

By comparing this with the formula for the product of roots, we have: 27 = a/1.

Therefore, the value of a is 27.

**Conclusion:**

The value of a in the quadratic equation x^2 - 12x + a = 0, where one root is thrice the other, is 27.

Therefore, the correct answer is option E) None of these.