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How would I approach this question. Should I find the values of alpha gamma and beta first and then substitute it in or expand it and use the formulars.

2 Answers

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The equation does not seem to have rational roots, it would be hard to find them.

The intention of the question was probably to use the relationship between coefficients of polynomials and their roots.

From thia you know the values of a + b + c, ab + bc + ca, abc, and (a) (b) can be expressed using them (using appropriate formulas)
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(x-α)(x-β)(x-γ) = x^(3) - (α+β+γ)x^(2) + (αβ+βγ+γα)x - αβγ

=> α+β+γ = -3, αβ+βγ+γα = -2, αβγ = 1

Hint for part a: expand (αβ+βγ+γα)(α+β+γ)

Hint for part b: expand (αβ+βγ+γα)^(2)

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