Properties of Polynomial Roots

Properties Of Polynomial Roots

In mathematics, a polynomial function is a function of the form

p(x) = a_0 + a_1 x + \cdots + a_n x^n, \quad x\in \mathbb{C}

where the coefficients are complex numbers and . The fundamental theorem of algebra states that polynomial p has n roots. The aim of this page is to list various properties of these roots.

Read more about Properties Of Polynomial Roots:  Continuous Dependence of Coefficients, Complex Conjugate Root Theorem, Radical Conjugate Roots, Bounds On Positive Polynomial Roots, Gauss–Lucas Theorem, Polynomials With Real Roots, Statistical Repartition of The Roots, See Also

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    —Ralph Waldo Emerson (1803–1882)

    “A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
    —Ralph Waldo Emerson (1803–1882)

    “To the young mind, every thing is individual, stands by itself. By and by, it finds how to join two things, and see in them one nature; then three, then three thousand; and so, tyrannized over by its own unifying instinct, it goes on tying things together, diminishing anomalies, discovering roots running underground, whereby contrary and remote things cohere, and flower out from one stem.”
    —Ralph Waldo Emerson (1803–1882)