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anonymous

  • one year ago

I have been told that two roots of the equation x^4 - 5x^2+2x=0 are 0 and -2. It then asks me to find the two other roots. The method I have been given tells me to use the constant and check all the factors of the constant with the equation to find the roots. Since there is no constant, will you please help me find what to do?

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  1. triciaal
    • one year ago
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    if the roots are a and b then (x-a) and (x-b) are factors of the polynomial. the highest exponent of the variable is 4 so there are 4 roots. f(x) = (x-a)(x-b)(x-c)(x-d) roots a, b, c, d f(x) divided by (x-a)(x-b) = (x-c)(x-d)

  2. triciaal
    • one year ago
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    can you see f(x)/x(x+2) = a quadratic to be factored ? when you factor that quadratic set = 0 solve to get the other roots

  3. triciaal
    • one year ago
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    |dw:1440434498406:dw|

  4. anonymous
    • one year ago
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    okay, I divided x^4-5x^2+2x by x-2. I got x^3+2x-x. Is that what I was supposed to do?

  5. triciaal
    • one year ago
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    root -2 factor (x-(-2) = x + 2 divide yes but by x +2 other factor x

  6. triciaal
    • one year ago
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    |dw:1440435257993:dw|

  7. anonymous
    • one year ago
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    When I divide the original equation by x+2 I get a remainder. Have I just made a mistake somewhere? I will send a photo of my working out...

  8. anonymous
    • one year ago
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  9. triciaal
    • one year ago
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    sorry I am blanking out what happens when you divide by x^2 + 2 ?

  10. anonymous
    • one year ago
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    Oh! I havnt done that yet! Sorry let me try that now

  11. triciaal
    • one year ago
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    you divide the quotient by x your constant was 8 factors of 8 are ? did not check your division remainder needed for "quadratic"

  12. triciaal
    • one year ago
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    the remainder theorem says if (x-a) is a factor then there is no remainder when you compute f(a)

  13. triciaal
    • one year ago
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    |dw:1440436446253:dw|

  14. anonymous
    • one year ago
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    Yes, I know that. I just dont understand how to get the other two roots. When trying to figure out how to do it myself I looked at the answers (back of my text book) and it said the answers were -1 and plus or minus the square root of 2. How do I get to those answers? Would it be better if I sent a picture of the questions from the actual book?

  15. triciaal
    • one year ago
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    |dw:1440436497477:dw|

  16. triciaal
    • one year ago
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    sorry I can't explain it better right now when I divide f(x) by x^2 had to add 1 to complete the quadratic so x-1 is a factor Quotient x^2 - 4 the factors are (x+2)(x-2)

  17. triciaal
    • one year ago
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    I guess from the method you need to use the remainder you have is -8 and one root is -2 so the other 4

  18. anonymous
    • one year ago
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    Ok, thanks very much for your help, unfortunately I still dont understand but maybe its because where I am its quite late so I will look at it again in the morning when you brain is fresh :). Thank you very much though

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