Methods of Design-Oriented Analysis: The Quadratic Equation Revisited

The conventional formula for quadratic roots suffers from two defects: it is High Entropy, and it is computationally inaccurate when two real roots are widely separated. An improved formula is suggested that overcomes both defects. Both roots are expressed in terms of a single parameter F that contains the radical sign and is a unique function of the single parameter Q that determines the nature of the roots. Both roots are computed in terms of F with the same computational accuracy, and the Low Entropy format exposes the useful design-oriented result that, for well-separated real roots, F approaches unity so that the radical disappears and both roots reduce to simple ratios of the original quadratic coefficients.