InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If α, β, γ are the roots of the equation x3 + ax2 + bx + c = 0, then what is α–1 + β–1 + γ–1 is equal to ? |
|
Answer» Given α, β, γ are the roots of the equation x3 + ax2 + bx + c = 0. Then, S1 = α + β + γ = \(-\frac{coefficient\,of\, x^2}{coefficient\,of\,x^3}\) = - a; S2 = αβ + βγ + αγ = \(-\frac{coefficient\,of\, x^2}{coefficient\,of\,x^3}\) = b S3 = αβγ = \(\frac{-constant\,term}{coefficient\,of\,x^3}\) = - c ∴ α–1 + β–1 + γ–1 = \(\frac{1}{α}\) + \(\frac{1}{β}\) + \(\frac{1}{γ}\) = \(\frac{βγ+αγ+αβ}{αβγ}\) = \(\frac{S_2}{S_3}\) = \(\frac{b}{-c}\) = \(-\frac{b}{c}.\) |
|