The roots of x^2 - 23x + 47 = 0 are a and b. Find (a - 2)(b - 2).
To start, let's find what a and b are. Using the quadratic formula, we see that a=(23+sqrt341)/2, and b=(23-sqrt341)/2. Now, plug that into what we want: ((23+sqrt341)/2-2)((23-sqrt341)/2-2). Multiply it out, and you get: 5.