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Round-off Error : Quadratic Equations


If b^2-4ac>0, the quadratic equation ax^2 + bx +c = zero has two real solutions x1, x2 given by the typical:
(1) X1 = (-b + sqrt(b^2 - 4ac))/2a and
(2) X2= (-b - sqrt(b^2 - 4ac))/2a
By rationalizing the numerator it is also given that:
(1A) X1 = -2c / (b + sqrt(b^2 - 4ac))
(2A) X2 = -2c / (b - sqrt(b^2 - 4ac))

Two Parts:
1. Choose two best solutions from above[(1), (2), (1A) or (2A)] for X1 and X2. Use 4 digit rounding arithmetic to find the approximate solutions X1 and X2 to

1.002x^2 - 11.01x + 0.01265 = 0.

2. Once the best approximations are found in step 1. If true solutions are X1 = 10.98687488 and X2 = .0011490757 what are the absolute and relative errors?

Thank you.

Solution Summary

Round-off errors and quadratic equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.