math polynomial questions using zeros?

A degree 4 polynomial with integer coefficients has zeros -2-5 i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1,

then the polynomial is??????

2 Answers

  • Anonymous
    1 decade ago
    Best Answer

    If the polynomial has real coefficients and one zero is -2 -5i then another is -2 + 5i. The other two zeros are both 1. So it is

    (x - 1)(x - 1)(x + 2 - 5i)(x + 2 + 5i)

    (x^2 - 2x + 1)(x^2 + 4x + 29)

    x^4 + 2x^3 + 22x^2 - 54x + 29

  • 3 years ago

    The quadratic formula (which all of us understand and love) will are looking forward to the roots of a quadratic. The cubic and quartic formulae are widespread in thought, yet I doubt everyone right here has them memorized or maybe has them obtainable. that's too elementary to ask a working laptop or laptop for the roots and characteristic it rattle them off those days. there isn't any quintic or bigger diploma formula which will resolve a accepted polynomial of diploma 5 or bigger and there on no account would be. that's been shown that there are roots of 5th order polynomials which would be unable to additionally be written in terms of roots! in case you prefer to examine up in this, the section that that's lined in is named Galois thought. it particularly is often senior college or first 365 days graduate artwork in arithmetic to realize it.

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