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Math Help - sums and products of roots

  1. #1
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    sums and products of roots

    i dont understand this question:
    in the quadratic equation x+mx+2=0, the roots are consecutive. find the values of m.
    i dont understand the part of the consecutive roots
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  2. #2
    MHF Contributor red_dog's Avatar
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    The roots are a and a+1, \ a\in\mathbb{Z}

    Then \left\{\begin{array}{ll}a+a+1=-m\\a(a+1)=2\end{array}\right.

    Solve the second equation, find a, then replace a in the first equation and find m.
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  3. #3
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    thanks for your help but i havent leant that so could you explain to me how that works?
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  4. #4
    ynj
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    Quote Originally Posted by pogiphilip View Post
    thanks for your help but i havent leant that so could you explain to me how that works?
    (-m)^2-4\cdot 2=(a+(a+1))^2-4a(a+1)=(a-(a+1))^2=1
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    i still dont understand what that is ynj
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  6. #6
    ynj
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    Quote Originally Posted by pogiphilip View Post
    i still dont understand what that is ynj
    Do you know Vieta's Theorem?
    if a quadratic equation ax^2+bx+c=0 have two roots \alpha,\beta, then a(x-\alpha)(x-\beta)=ax^2+bx+c\Leftrightarrow ax^2-a(\alpha+\beta)x+a\alpha\beta=0
    Thus \alpha+\beta=-\frac{b}{a},\alpha\beta=\frac{c}{a}to keep all the coefficient identical.
    So a+(a+1)=-m,a(a+1)=2, (-m)^2-4\cdot 2=(a+(a+1))^2-4a(a+1)=(a-(a+1))^2=1, Then you can solve m!
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  7. #7
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    but also the question says to use roots that are consecutive?, and i don't know vieta's theorem.
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  8. #8
    ynj
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    Quote Originally Posted by pogiphilip View Post
    but also the question says to use roots that are consecutive?, and i don't know vieta's theorem.
    That means two roots are in the form a,a+1. Vieta's Theorem has been proved in my previous post.
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  9. #9
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    thank you for your help and i think i figured it out. thanks ynj and red_dog
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  10. #10
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    also what are the roots if the two roots are consecutive?
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  11. #11
    ynj
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    Quote Originally Posted by pogiphilip View Post
    also what are the roots if the two roots are consecutive?
    you may use formula to solve it .......
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