A quadratic equation x² - 12x + a = 0 has roots where one root is three times the other. What is the value of a?

Explanation

Let the roots be x and 3x. The sum of the roots is x + 3x = 4x, which equals 12 (from the equation's coefficient). Solving 4x = 12 gives x = 3. The product of the roots is x * 3x = 3x² = 3 * 3² = 27. Therefore, the value of a is 27.