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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. sauravshakya
    • 3 years ago
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    AT FIRST. do u know what a degree of polynomial means.

  2. moongazer
    • 3 years ago
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    \[3x^3+(3x^2/2)−(3x/2)+(3/2)\] is this correct?

  3. moongazer
    • 3 years ago
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    for 1.?

  4. sauravshakya
    • 3 years ago
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    simplify that.

  5. moongazer
    • 3 years ago
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    Is my answer correct?

  6. sauravshakya
    • 3 years ago
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    |dw:1343207441484:dw|

  7. moongazer
    • 3 years ago
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    how about for no. 2 could you help me?

  8. sauravshakya
    • 3 years ago
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    can u simplify this plz

  9. sauravshakya
    • 3 years ago
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    I DONT THINK YOUR ANSWER IS CORRECT.

  10. moongazer
    • 3 years ago
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    ok

  11. sauravshakya
    • 3 years ago
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    FOR NUMBER 2) do u know factor theorem

  12. moongazer
    • 3 years ago
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    could I make \[(x-1/2) -------> (2x-1)\] ????????

  13. sauravshakya
    • 3 years ago
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    |dw:1343207772794:dw|

  14. sauravshakya
    • 3 years ago
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    NOW do u know factor theorem? and did u get answer for 1)

  15. moongazer
    • 3 years ago
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    \[3x^3-(3x^2/2)−3x−(3/2)\]

  16. moongazer
    • 3 years ago
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    am I correct now?

  17. sauravshakya
    • 3 years ago
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    NOPE.

  18. sauravshakya
    • 3 years ago
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    BUT U R VERY CLOSE

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

  20. sauravshakya
    • 3 years ago
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    u just made the sign mistake

  21. moongazer
    • 3 years ago
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    could I make (x-1/2) into (2x-1) because my teacher said there should be no fractions?

  22. moongazer
    • 3 years ago
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    @sauravshakya

  23. sauravshakya
    • 3 years ago
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    |dw:1343208282102:dw|

  24. sauravshakya
    • 3 years ago
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    is the correct answer

  25. moongazer
    • 3 years ago
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    could I make (x-1/2) into (2x-1) ??????

  26. sauravshakya
    • 3 years ago
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    NOPE because|dw:1343208355724:dw|

  27. sauravshakya
    • 3 years ago
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    but if |dw:1343208386811:dw|

  28. moongazer
    • 3 years ago
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    that's what I mean for the second part

  29. sauravshakya
    • 3 years ago
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    because|dw:1343208443188:dw|

  30. moongazer
    • 3 years ago
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    isn't that it is zero so that it is possible?

  31. moongazer
    • 3 years ago
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    |dw:1343205903760:dw|

  32. sauravshakya
    • 3 years ago
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    IF it is equal to zero then yes u can because |dw:1343208534245:dw|

  33. moongazer
    • 3 years ago
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    |dw:1343205945423:dw|

  34. sauravshakya
    • 3 years ago
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    so what?

  35. moongazer
    • 3 years ago
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    I got the correct answer :)

  36. sauravshakya
    • 3 years ago
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    and what is that

  37. moongazer
    • 3 years ago
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    it mean that there zeroes are both 1/2

  38. moongazer
    • 3 years ago
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    so you can use either of the two?

  39. sauravshakya
    • 3 years ago
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    yeah. BUT only in that case. U cannot use this in simplification.

  40. sauravshakya
    • 3 years ago
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    AND NOW SHALL WE BEGIN NO. 2

  41. moongazer
    • 3 years ago
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    yup :)

  42. sauravshakya
    • 3 years ago
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    do u know factor theorem.

  43. moongazer
    • 3 years ago
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    wait I am trying to solve 1 with (2x-1) :)

  44. moongazer
    • 3 years ago
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    I got the same answer :)

  45. moongazer
    • 3 years ago
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    I know factor theorem. If the remainder when dividing P(x) by D(x) is zero, then D(x) is a factor of P(x). P(x) is any polynomial D(x) is the divisor being a factor means it is included in multiplying.

  46. moongazer
    • 3 years ago
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    is that correct? could you improve my definition of factor ?

  47. sauravshakya
    • 3 years ago
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    No u r defination is correct. And can u use this to solve this problem

  48. moongazer
    • 3 years ago
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    how I am confused with the question?

  49. moongazer
    • 3 years ago
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    I am thinking of distributing -3 to x

  50. moongazer
    • 3 years ago
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    but I can't explain why it is correct :)

  51. sauravshakya
    • 3 years ago
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    your 2 number question simply means that if u divide P(x) by (x+3) then remainder is zero. |dw:1343209619170:dw|

  52. moongazer
    • 3 years ago
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    ohh, I think it also has remainder theorem? :)

  53. sauravshakya
    • 3 years ago
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    YEAH.

  54. sauravshakya
    • 3 years ago
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    now can u

  55. moongazer
    • 3 years ago
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    |dw:1343207190855:dw|

  56. moongazer
    • 3 years ago
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    I added =0 so that the remainder will be equal to zero making (x+3) a product ?

  57. sauravshakya
    • 3 years ago
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    solve for k

  58. moongazer
    • 3 years ago
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    am I correct with my reason?

  59. sauravshakya
    • 3 years ago
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    yeah

  60. moongazer
    • 3 years ago
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    k=1/2

  61. moongazer
    • 3 years ago
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    @sauravshakya thank you very much for your help :)

  62. sauravshakya
    • 3 years ago
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    U r WELCOME. AND best of luck

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