Finding Square Roots and Solving Quadratic Equations

Now, the formula does not provide us with a solution that is written in decimal form; to get such a solution we need to evaluate the above expression. To this end, since most computers perform additions, subtractions, multiplications, and even divisions very fast, we should focus on the need to take a squareroot. In short, the “explicit” solution for the quadratic equation actually reduces our problem to finding an algorithm for computing squareroots. Even if we have such an algorithm, we have to ask if using the quadratic formula is the most efficient way to solve this equation; in other words, whether the best algorithm for finding squareroots is superior to the best algorithm that solves the quadratic equation without using the formula. As we shall show now, we can extend the powerful square root algorithm we proposed in the last lecture so that it solves general quadratic equations, making the use of the quadratic formula (2) unnecessary (and, in fact, inefficient).