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Numerical methods Use five-digit arithmetic to find the roots of the equation x² - 5000.002x + 10 = 0 by considering Equations 3.12 and 3.13 in the following image:

Numerical methods Use five-digit arithmetic to find the roots of the equation x² - 5000.002x + 10 = 0 by considering Equations 3.12 and 3.13 in the following image:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 81E
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Numerical methods Use five-digit arithmetic to find the roots of the equation x² - 5000.002x + 10 = 0 by considering Equations 3.12 and 3.13 in the following image: Subtractive Cancellation. This term refers to the round-off induced when subtracting two nearly equal floating-point numbers. One common instance where this can occur involves finding the roots of a quadratic equation or parabola with the quadratic formula, -b± √b²-4ac XI x2 = (3.12) 2a For cases where b² > 4ac, the difference in the numerator can be very small. In such cases, double precision can mitigate the problem. In addition, an alternative formulation can be used to minimize subtractive cancellation, X1 -2c = x₂ b ± √b² - 4ac (3.13)
Transcribed Image Text:Numerical methods Use five-digit arithmetic to find the roots of the equation x² - 5000.002x + 10 = 0 by considering Equations 3.12 and 3.13 in the following image: Subtractive Cancellation. This term refers to the round-off induced when subtracting two nearly equal floating-point numbers. One common instance where this can occur involves finding the roots of a quadratic equation or parabola with the quadratic formula, -b± √b²-4ac XI x2 = (3.12) 2a For cases where b² > 4ac, the difference in the numerator can be very small. In such cases, double precision can mitigate the problem. In addition, an alternative formulation can be used to minimize subtractive cancellation, X1 -2c = x₂ b ± √b² - 4ac (3.13)
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