Question

If α ,β and g are the roots of 7x³ − x − 2 = 0, then find the value of ∑(α/β + β/α).

Answer 1

∑α = 0. ∑αβ =  - (1/7) and α β γ = 2/7

Now, (α + β + γ)(1/α + 1/β+ 1/ γ) = 3 +  ∑(α/β + β/α).on expansion. Therefore,

3 +  ∑(α/β + β/α) = 0.  (since α + β  + γ = 0)

⇒  ∑(α/β + β/α)  = -3