(Easy/Difficult Problem Pairs) Write a computer program to obtain the power form of a po...

(Easy/Difficult Problem Pairs) Write a computer program to obtain the power form of a polynomial from its roots. Let the roots be r₁, r₂, . . . , r_n. Then (except for a scalar factor) the polynomial is the product

p(x) = (x − r₁)(x − r₂) · · · (x − r_n).

Find the coefficients in the expression

Test your code on the Wilkinson polynomials in Computer Exercises 3.1.10 and 3.3.9. Explain why this task of getting the power form of the polynomial is trivial, whereas the inverse problem of finding the roots from the power form is quite difficult.