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anonymous

  • one year ago

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -14, and 5 + 8i

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    If 5 + 8i is a zero, then 5 - 8i must also be a zero. Now combine the zeros and multiply \[f(x)=(x-4)(x+14)(x-5+8i)(x-5-8i)\]

  3. anonymous
    • one year ago
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    f(x)=(x−4)(x+14)(x−5+8i)(x−5−8i)

  4. anonymous
    • one year ago
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    x^4-9x^3

  5. anonymous
    • one year ago
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    how would i do the rest

  6. anonymous
    • one year ago
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    id either get 725x or 1450x

  7. anonymous
    • one year ago
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    I'm not sure how you got x^4-9x^3. You need to multipliy these using the distributive property. Start with (x−5+8i)(x−5−8i) to eliminate the imaginary parts

  8. anonymous
    • one year ago
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    x^2-5x-8ix-5x+25+40i+8ix-40i

  9. anonymous
    • one year ago
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    you're missing -64i², which simplifies to 64. Now combine like terms. All the parts with i will cancel out

  10. anonymous
    • one year ago
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    x^2-10x+25-64i^2+81x

  11. anonymous
    • one year ago
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    there's no 81x. Just \(x^2-10x+25-64i^2\) and -64i² = 64. So once you combine it's \[x^2-10x+89\]

  12. anonymous
    • one year ago
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    Set that off to the side and multiply (x-4)(x+14)

  13. anonymous
    • one year ago
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    x^2+14x-4x-56 x^2+10x-56

  14. anonymous
    • one year ago
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    Right :) so now all that's left is to multiply the two quadratics \[(x^2-10x+89)(x^2+10x-56)\]

  15. anonymous
    • one year ago
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    (x2−10x+89)(x2+10x−56) x^4+10x^3-56x^2-10x^2+560+89X^2+890x-4989

  16. anonymous
    • one year ago
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    x^4+10x^3+23x+890x-4429

  17. anonymous
    • one year ago
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    you missed a term (-10x)(10x) and 89*56 = 4984. Altogether it should be \[x^4+10x^3-56x^2-10x^3-100x^2+560x+89x^2+890x-4984\]

  18. anonymous
    • one year ago
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    x^4+67x^2+1450x-4984

  19. anonymous
    • one year ago
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    C thank you!

  20. anonymous
    • one year ago
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    \[x^4-67x^2+1450x-4984\] yes C

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