A New Property Related to the Roots of an
Equation

Tuhin Bose

doi:https://doi.org/10.14445/22315373/IJMTT-V60P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

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