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anonymous

  • one year ago

The value -2 is a lower bound for the zeros of the function shown below. f(x)=4x^3-12x^2-x+15

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  1. anonymous
    • one year ago
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    True or false?

  2. UsukiDoll
    • one year ago
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    all positive values are upper bound all negative values are lower bound

  3. anonymous
    • one year ago
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    is it false? I use synthetic division right? I got 4, -20, 39, 171

  4. UsukiDoll
    • one year ago
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    can you draw that synthetic division for me?

  5. anonymous
    • one year ago
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    |dw:1437277905106:dw| sorry it's kind of hard to read but i just realized i messed up earlier haha is it still false though?

  6. anonymous
    • one year ago
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    because not everything is negative??

  7. anonymous
    • one year ago
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    i don't get it :/

  8. UsukiDoll
    • one year ago
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    \[f(x)=4x^3-12x^2-x+15 \] is our function oh I see we use -2 for synthetic division

  9. UsukiDoll
    • one year ago
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    |dw:1437278252692:dw|

  10. UsukiDoll
    • one year ago
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    so the first entry should go down |dw:1437278300525:dw|

  11. UsukiDoll
    • one year ago
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    then we multiply -2 x 4

  12. UsukiDoll
    • one year ago
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    |dw:1437278367948:dw| then use addition we should get -20

  13. UsukiDoll
    • one year ago
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    now -2 x -20 = 40 |dw:1437278417562:dw| and then we should have 39

  14. UsukiDoll
    • one year ago
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    |dw:1437278454846:dw|

  15. anonymous
    • one year ago
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    yup thats what i got too!

  16. UsukiDoll
    • one year ago
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    so now we can re-write this the last part should be \[\frac{-63}{x-2} \] because -63 is the remainder

  17. UsukiDoll
    • one year ago
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    ok I'm going backwards in writing this since it's been a while

  18. UsukiDoll
    • one year ago
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    ack wrong sign \[4x^2 -20x+39-\frac{63}{x+2}\]

  19. anonymous
    • one year ago
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    so would it be true or false?

  20. UsukiDoll
    • one year ago
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    since -2 < 0 and the signs during the synthesis division alternate, we have a lower bound for real roots of the function.

  21. anonymous
    • one year ago
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    ohh. i get it, thank you :)

  22. UsukiDoll
    • one year ago
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    geez what is with my writing? I meant signs during the synthetic division alternate XD

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