(a) Consider the polynomial p = r - 8r + 26.r 40.r + 25 (i)...

 

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(a) Consider the polynomial p = r - 8r + 26.r² – 40.r + 25 (i) Find all the multiple roots of the polynomial p or show that it has none. (i) Do there exist polynomials q,r e Qlr] such that dp = 1? IP +r dr You must justify your answer. (b) Write the symmetric polynomial f = r +y+ 2 +6ryz in terms of elementary symmetric polynomials in the variables r, y, z. (a) Consider the polynomial p = r - 8r + 26.r² – 40.r + 25 (i) Find all the multiple roots of the polynomial p or show that it has none. (i) Do there exist polynomials q,r e Qlr] such that dp = 1? IP +r dr You must justify your answer. (b) Write the symmetric polynomial f = r +y+ 2 +6ryz in terms of elementary symmetric polynomials in the variables r, y, z.