The cubic equation x 3 5x 2 + 1 = 0 has roots , , .

Question:

The cubic equation x3 – 5x2 + 1 = 0 has roots α, β, γ.

a. Find the values of S1 and S3.

Another cubic equation has roots α2, β2, γ2.

b. Find the cubic equation with these roots.

c. Hence, or otherwise, determine the result of S6.

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