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    Roots

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    1. Find the number of real roots and imaginary roots:
    f(x)=10x^5-34x^4-5x^3-8x^2+3x+8

    2. Find all zeros:
    f(x)=x^4+2x^3+5x^2+34x+30

    3. Find all roots:
    f(x)=x^3-7x^2-17x-15; 2 + i

    4. Find all roots:
    f(x)=x^4-6x^3+12x^2+6x-13; 3 + 2i

    The 5th problem is attached.

    Please answer the questions above and show the work done. Thank you!

    © BrainMass Inc. brainmass.com March 4, 2021, 5:52 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/real-roots-imaginary-roots-15269

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    1.Find the number of real roots and imaginary roots:

    In order to find all real roots, we must count the number of times the sign changes in the equation for f(x). Thus, there are two sign changes, from +10 to -34, and -8 to +3. Thus, there are two positive real roots.

    In order to find the number of negative real roots, we need to count the sign changes in f(-x). Thus,

    Thus, the sign changes from -34 to +5, +5 to -8, and ...

    Solution Summary

    This shows how to find real and imaginary roots for polynomials up to degree 5.

    $2.19

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