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anonymous

  • one year ago

MEDAL AND FAN!!!! Which of the following represents the zeros of f(x) = 3x3 − 10x2 − 81x + 28

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  1. UsukiDoll
    • one year ago
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    \[f(x) = 3x^3-10x^2-81x+28 \] this?

  2. UsukiDoll
    • one year ago
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    if we need to find 0's then we need the rational root test.

  3. UsukiDoll
    • one year ago
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    The Rational Roots Test (also known as Rational Zeros Theorem) allows us to find all possible rational roots of a polynomial. Suppose "a" is root of the polynomial P(x) that means P(a) = 0. In other words, if we substitute "a" into the polynomial P(x) and get zero it means that the input value is a root. so we take the last term, 28, and find all factors of 28 which is 1,2,4,7,14,28. We also have to take the negative versions as well. So, 1,-1,2,-2,4,-4,7,-7,14,-14,28,-28 just plug these numbers into the equation and stop once you have a 0 there could be more than one root, just one, or none. If we don't have any roots, the test fails.

  4. anonymous
    • one year ago
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    is the answer 7, -4, 1/3

  5. alekos
    • one year ago
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    but the last root lies somewhere between 0 and 1 and I think 1/3 is pretty close

  6. anonymous
    • one year ago
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    answer choices 7,-4,1/3 7,-4,-1/3 7,4,1/3 7,4,-1/3

  7. UsukiDoll
    • one year ago
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    hmmm.... let x = 7,4, or -4 and plug it into the equation ... one of them has to produce a zero .we may have to go further like long division to grab the remaining roots

  8. anonymous
    • one year ago
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    im pretty sure it is the last choice

  9. UsukiDoll
    • one year ago
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    did you test it out?

  10. anonymous
    • one year ago
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    kind of

  11. UsukiDoll
    • one year ago
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    because there's a negative root.. and that number is not -1/3

  12. UsukiDoll
    • one year ago
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    so that knocks out two choices.

  13. anonymous
    • one year ago
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    that means it is the third choice because after you test it out it gives you the third choice

  14. UsukiDoll
    • one year ago
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    no

  15. alekos
    • one year ago
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    negative root is x=-4

  16. UsukiDoll
    • one year ago
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    mhm ^

  17. anonymous
    • one year ago
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    oops i think i know the answer for this question can you help me with another

  18. UsukiDoll
    • one year ago
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    yeah sure. you actually had the right answer 10 minutes ago XD

  19. anonymous
    • one year ago
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    Which of the following is a polynomial with roots 5, 4i, and −4i

  20. anonymous
    • one year ago
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    f(x) = x^3-5x^2+20x-16 f(x) = x^3-5x^2+16x-80 f(x)=x^3-20x^2+5x-16 f(x) = x^3-16x^2+80x-5

  21. UsukiDoll
    • one year ago
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    wow... it's like we have to use the roots given and plugging in it into the function having x = 5 will make it easier though.

  22. anonymous
    • one year ago
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    so plug 5 for each one

  23. UsukiDoll
    • one year ago
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    try let x = 5 for the second function

  24. UsukiDoll
    • one year ago
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    yeah for each one, but I think I've weeded it out x=5 for the second function

  25. anonymous
    • one year ago
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    i think i can take out the 2nd one and also the the first one

  26. UsukiDoll
    • one year ago
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    first one is nasty... x.x

  27. anonymous
    • one year ago
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    so that is definitely eliminated

  28. UsukiDoll
    • one year ago
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    oh yeah... not to mention that the real root is x=1... not what we need.

  29. anonymous
    • one year ago
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    the answer is the third one

  30. UsukiDoll
    • one year ago
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    umm are you sure?

  31. anonymous
    • one year ago
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    im pretty sure

  32. UsukiDoll
    • one year ago
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    the real root I'm getting for that third choice is really bad ... same with the imaginary... the real root is approx.. 20.. we need x = 5,4i,-4i cross that out

  33. anonymous
    • one year ago
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    im feeling that my work shows that it is the answer

  34. anonymous
    • one year ago
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    the last one

  35. UsukiDoll
    • one year ago
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    try plugging x = 5 for the second function you have and tell me if your result is 0 f(x) = x^3-5x^2+16x-80

  36. anonymous
    • one year ago
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    yes

  37. UsukiDoll
    • one year ago
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    then that's the function. since the result became 0... for x = 5... then the roots x =4i, -4i work as well.

  38. anonymous
    • one year ago
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    thanks

  39. UsukiDoll
    • one year ago
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    you're welcome :)

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