Select a routine from your program library to solve polynomial equations and use it to f...

Select a routine from your program library to solve polynomial equations and use it to find the roots of the equation

The correct roots are the integers 1, 2, . . . , 8. Next, solve the same equation when the coefficient of x⁷ is changed to −37. Observe how a minor perturbation in the coefficients can cause massive changes in the roots. Thus, the roots are unstable functions of the coefficients. (Be sure to program the exercise to allow for complex roots.) Cultural Note: This is a simplified version of Wilkinson’s polynomial, which is found in Computer Exercise 3.3.9.