Final answer:
The problem involves finding the other root of the quadratic equation x2 - 14x + w = 0 given that one root is 6. Using the sum of the roots formula for quadratic equations, we determine the other root to be 8.
Step-by-step explanation:
The question asks about one of the roots of a quadratic equation, which reflects a mathematical problem. If one root of the quadratic equation x2 - 14x + w = 0 is 6, then we can find the other root by using the properties of quadratic equations. Specifically, if x1 and x2 are the roots of the quadratic equation ax2 + bx + c = 0, then sum of the roots is -b/a, and the product of the roots is c/a. Therefore, if we know that x1 = 6 and a = 1 (since the coefficient of x2 is 1), we can use the sum of the roots formula to find x2.
To calculate this:
x1 + x2 = -(-14)/1
x2 = 14 - x1
x2 = 14 - 6
x2 = 8
Therefore, the other root of the quadratic equation is 8.