Question: Let p(x) = -x3 + cx2 + (c + 3)x + 1, where c is a real number. Let C denote the companion matrix of

Let p(x) = -x3 + cx2 + (c + 3)x + 1, where c is a real number. Let C denote the companion matrix of p(x),
Let p(x) = -x3 + cx2 + (c + 3)x

and let

Let p(x) = -x3 + cx2 + (c + 3)x

(a) Compute A-1CA.
(b) Use the result from part (a) to prove that p(x) will have only real roots regardless of the value of c.

c c+3 1 C= 1 0 0 2 1-1 c+2 I I -c-I A=

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