Chapter 1.2, Problem 15ES

Use four-digit rounding arithmetic and the formulas (1.1), (1.2), and (1.3) to find the most accurate approximations to the roots of the following quadratic equations. Compute the absolute errors and relative errors.

1. a. $\frac{1}{3}{x}^2-\frac{123}{4}x+\frac{1}{6}=0$
2. b. $\frac{1}{3}{x}^2+\frac{123}{4}x-\frac{1}{6}=0$
3. c. 1.002x² − 11.01x + 0.01265 = 0
4. d. 1.002x² + 11.01x + 0.01265 = 0