Suppose x₁ and x2 are the roots of the quadratic equation x²+bx+c = 0. (a) Use implicit differentiation to compute dx/db. (b) We know that the roots are 2= 1/(-b² X1,2 = (-b± √b²-4c). Differentiate this expression with respect to b and show that the answer is equivalent to the one you obtained in (a). (c) Find values of b and c for which the roots are very sensitive to small changes in b, and values for which they are not very sensitive.

Suppose x₁ and x2 are the roots of the quadratic equation x²+bx+c = 0. (a) Use implicit differentiation to compute dx/db. (b) We know that the roots are 2= 1/(-b² X1,2 = (-b± √b²-4c). Differentiate this expression with respect to b and show that the answer is equivalent to the one you obtained in (a). (c) Find values of b and c for which the roots are very sensitive to small changes in b, and values for which they are not very sensitive.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter3: Introduction To Linear Programming

Section: Chapter Questions

Problem 59RP

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