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Volume 60 | Number 1 | Year 2018 | Article Id. IJMTT-V60P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P508
A New Property Related to the Roots of an
Equation
Tuhin Bose
Citation :
Tuhin Bose, "A New Property Related to the Roots of an
Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 1, pp. 43-44, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P508
Abstract
If all roots of the 𝑛 degree equation 𝑎0𝑥
𝑛 + 𝑎1𝑥
(𝑛−1) + 𝑎2𝑥
(𝑛−2) + ⋯ + 𝑎𝑛 = 0 [Where 𝑛 ∈ ℕ and
𝑎0
, 𝑎1
, … , 𝑎𝑛 are real numbers and 𝑎0 > 0] are positive real numbers then,
𝑎𝑖𝑎(𝑛−𝑖)
𝑎𝑛
≥ [
𝑛
𝑖
]
2𝑎0
[For all 𝑖 ∈ ℕ and 1 ≤ 𝑖 ≤ 𝑛]
Keywords
Cauchy-Schwarz inequality,Roots,Equation
References
[1] An Excursion In Mathematics
[2] Internet