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moongazer

  • 3 years ago

1.) Find a polynomial of degree that has zeros 1, -1 and 1/2 and whose leading coefficient is 3. 2.) Find the value of k such that x+3 is a product of P(x) = x^2 - 10kx + 6

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  1. moongazer
    • 3 years ago
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    My answer for no. 1 is \[3x^3 -( 3x^2/2) - 3x + (3/2)\] but my teacher said there should be no fractions

  2. lgbasallote
    • 3 years ago
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    then multiply all the terms by 2(the denominator) to get rid of the fraction

  3. moongazer
    • 3 years ago
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    but the leading coefficient will not be 3???

  4. moongazer
    • 3 years ago
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    @saifoo.khan

  5. moongazer
    • 3 years ago
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    could you help me?

  6. saifoo.khan
    • 3 years ago
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    |dw:1343106002554:dw|

  7. moongazer
    • 3 years ago
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    What does it mean by leading coefficient?

  8. saifoo.khan
    • 3 years ago
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    http://4.bp.blogspot.com/_lvMAEEKgEx8/TM6ebuxxeYI/AAAAAAAAAhA/PMyxtcHq5hI/s320/a.gif

  9. moongazer
    • 3 years ago
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    isn't that your answer does not have a leading coefficient of 3 ?

  10. saifoo.khan
    • 3 years ago
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    you did a mistake in multiplying.

  11. saifoo.khan
    • 3 years ago
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    (x-1)(x+1)(x-1/2) = 0 try again.

  12. moongazer
    • 3 years ago
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    I'll do it again :)

  13. saifoo.khan
    • 3 years ago
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    Sure.

  14. moongazer
    • 3 years ago
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    I did (x-1)(x+1)(2x-1) = 0 is it the same as (x-1)(x+1)(x-1/2) = 0 ??

  15. saifoo.khan
    • 3 years ago
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    yup.

  16. moongazer
    • 3 years ago
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    I got\[x^3+( x^2/2) -(x/2)+(1/2)\] I checked it twice :)

  17. moongazer
    • 3 years ago
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    @saifoo.khan is this correct?

  18. saifoo.khan
    • 3 years ago
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    Now this is correct!! :D

  19. saifoo.khan
    • 3 years ago
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    NOw get rid of 2 in the denominators, multiply the whole expression by 2.

  20. moongazer
    • 3 years ago
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    \[2x^3 + x^2 - x + 1\]

  21. moongazer
    • 3 years ago
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    How will I make it into 3?

  22. saifoo.khan
    • 3 years ago
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    Are decimals allowed?

  23. moongazer
    • 3 years ago
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    he said there is no fractions

  24. saifoo.khan
    • 3 years ago
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    SInce your teacher said NO FRACTIONS.

  25. saifoo.khan
    • 3 years ago
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    :D

  26. moongazer
    • 3 years ago
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    that's why I am confused :) or maybe I misheard him :)

  27. saifoo.khan
    • 3 years ago
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    Possibly..

  28. saifoo.khan
    • 3 years ago
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    We can multiply the equation by 1.5 to make the leading coef as 3. :D

  29. moongazer
    • 3 years ago
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    maybe he is referring to (2x-1) and (x-1/2)

  30. saifoo.khan
    • 3 years ago
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    2x-1 and x-1/2 is same.

  31. saifoo.khan
    • 3 years ago
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    are* same.

  32. moongazer
    • 3 years ago
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    so my answer I think is \[3x^3 + (3x^2/2) - (3x/2) + (3/2)\] that's the only expression I can have to make the leading coefficient equal to 3

  33. moongazer
    • 3 years ago
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    is that correct?

  34. saifoo.khan
    • 3 years ago
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    3x^3 + 1.5x^2 - 1.5x + 1.5 NO FRACTIONS!!! :D

  35. moongazer
    • 3 years ago
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    lol, I'll just include that to my answer :)

  36. moongazer
    • 3 years ago
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    how about for the second one ?

  37. saifoo.khan
    • 3 years ago
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    HAHA. http://funny-pictures-blog.com/wp-content/uploads/funny-pictures/Like-a-boss.jpg

  38. saifoo.khan
    • 3 years ago
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    That question looks like a challenge!!

  39. moongazer
    • 3 years ago
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    it should be P(x) = x^2 - 10kx + 6

  40. moongazer
    • 3 years ago
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    it had a typo :)

  41. saifoo.khan
    • 3 years ago
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    Find the value of k such that x+3 is a product of P(x) = x^2 - 10kx + 6 (-3)^2 - 10k(-3) + 6 = 0 9 + 30 k + 6 = 0

  42. moongazer
    • 3 years ago
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    I got k = 1/2 but why did you made x into -3?

  43. saifoo.khan
    • 3 years ago
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    Because since it's a product of it, the remainder is 0.

  44. saifoo.khan
    • 3 years ago
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    So we insert the factor and set the equation = 0.

  45. moongazer
    • 3 years ago
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    Thanks, I understand it :)

  46. saifoo.khan
    • 3 years ago
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    Great. Welcome.

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