Let p(x) = x3 + cx2 + (c + 3)x + 1, where c is a real number. Let C = c c+3 1 1 0 0 0 1
Chapter 6, Problem 25(choose chapter or problem)
Let p(x) = x3 + cx2 + (c + 3)x + 1, where c is a real number. Let C = c c+3 1 1 0 0 0 1 0 and let A = 1 2 c 3 1 1 c + 2 1 1 c 1 (a) Compute A1CA. (b) Show that C is the companion matrix of p(x) and use the result from part (a) to prove that p(x) will have only real roots, regardless of the value of c. 2
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