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anonymous

  • one year ago

Find a cubic function with the given zeros. √6 , -√6, -3

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  1. anonymous
    • one year ago
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    @amistre64

  2. amistre64
    • one year ago
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    what do we know about zeros of a function, what do they do to the function?

  3. anonymous
    • one year ago
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    they mark the intercepts?

  4. amistre64
    • one year ago
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    yeah, they do mark the x intercepts. but something more useful to is is that the make the function, equal out to zero.

  5. amistre64
    • one year ago
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    now, another thing we should know, is that anything times 0, is equal to 0 ... right?

  6. anonymous
    • one year ago
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    yep

  7. amistre64
    • one year ago
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    so, would you agree that if x=a, then x-a = 0 ?

  8. anonymous
    • one year ago
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    yes

  9. amistre64
    • one year ago
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    given any number of roots, we can then create a function: say the roots are a,b,c let f(x) = (x-a)(x-b)(x-c) will f(a)=0? f(b)=0? and f(c)=0?

  10. anonymous
    • one year ago
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    okay, so we have to find which one ?

  11. amistre64
    • one year ago
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    we simply need to expand (multiply thru, distribute) this into the cubic format.

  12. amistre64
    • one year ago
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    let f(x) = (x-a)(x-b)(x-c) for the stated zeros; a,b, and c how would we expand this into a cubic format?

  13. anonymous
    • one year ago
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    multiply it out

  14. amistre64
    • one year ago
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    can you show me how it looks when we multiply it out?

  15. anonymous
    • one year ago
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    http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427elr1dfihajj is that right?

  16. amistre64
    • one year ago
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    that link is not working for my browser :/ (x-c)(xx-bx-ax+ba) xxx-bxx-axx+bax -cxx+bcx+cax-abc x^3 -(a+b+c)xx^2 +(ab+ac+bc)x -abc

  17. amistre64
    • one year ago
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    let a=sqrt(6), b=-sqrt(6), and c=-3

  18. anonymous
    • one year ago
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    ok

  19. anonymous
    • one year ago
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    btw the link says x^3 + 3x^2 -6x -18

  20. amistre64
    • one year ago
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    a+b+c = -3, so --3 = 3 is fine ab+ac+bc = -6, thats good and -(--6.3) is -18

  21. anonymous
    • one year ago
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    so now we just combine them to get the function

  22. amistre64
    • one year ago
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    that IS the function ..

  23. amistre64
    • one year ago
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    f(x) = x^3 +3x^2-6x-18

  24. amistre64
    • one year ago
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    any scaled form of this also works ... so this is not a unique solution

  25. anonymous
    • one year ago
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    i see, thanks so much!

  26. amistre64
    • one year ago
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    goodluck

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