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    Round-off Error : Quadratic Equations

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    GIVEN

    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))

    PROBLEM
    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.

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    https://brainmass.com/math/basic-algebra/round-error-quadratic-equations-163260

    Solution Preview

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    If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions x1, x2 given by the typical:
    (1) x1 = , and
    (2) x2 =
    By rationalizing the numerator it is also given that:
    (1a) x1 =
    (2a) ...

    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.

    $2.49

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