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maheshmeghwal9 Group Title

If x^3+ax+b=0, & a,b belongs to real numbers, b is not equal to zero.Then, why a<0,since it is the a statement which holds true.And all the roots of this equation are real.

  • 2 years ago
  • 2 years ago

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  1. blockcolder Group Title
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    So your question is...?

    • 2 years ago
  2. maheshmeghwal9 Group Title
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    my ques is why a<0.under what coditions?

    • 2 years ago
  3. maheshmeghwal9 Group Title
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    sorry,under what conditions?

    • 2 years ago
  4. maheshmeghwal9 Group Title
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    this is a question of theory of equations.

    • 2 years ago
  5. blockcolder Group Title
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    Do you have other assumptions on the cubic equation, like, how many solutions does it have, or other stuff like that?

    • 2 years ago
  6. maheshmeghwal9 Group Title
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    no I don't know about the solutions but I know that this is a thoughtful question.

    • 2 years ago
  7. maheshmeghwal9 Group Title
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    this is only verify and prove question.

    • 2 years ago
  8. veramath Group Title
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    The statement is not complete. For example: we say the standard form of quadratic equation is \[ax^2+bx+c=0, where a, b, c \in R \] and a, b not both zero

    • 2 years ago
  9. maheshmeghwal9 Group Title
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    but question is is true because my sir has solved it and i have lost that paper on which sir solved that.

    • 2 years ago
  10. freckles Group Title
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    I don't understand the question. You want us to solve for x? Is that what your asking?

    • 2 years ago
  11. cinar Group Title
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    http://www.sosmath.com/algebra/factor/fac11/fac11.html

    • 2 years ago
  12. maheshmeghwal9 Group Title
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    what is this?

    • 2 years ago
  13. maheshmeghwal9 Group Title
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    one more thing about this quetion

    • 2 years ago
  14. maheshmeghwal9 Group Title
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    all the roots of this cubic equations are real

    • 2 years ago
  15. freckles Group Title
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    Oh ok now the question makes more sense. lol/

    • 2 years ago
  16. freckles Group Title
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    Omg I'm sorry. My page got killed when I was typing all of that. :(

    • 2 years ago
  17. maheshmeghwal9 Group Title
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    np!

    • 2 years ago
  18. freckles Group Title
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    @foolformath what do you think of this problem? For some reason I was thinking about finding f' And I found critical numbers pm sqrt(-a/3) I found it is increasing on (-inf,-sqrt(-a/3)) and (sqrt(-a/3),inf) and decreasing on (-sqrt(-a/3),sqrt(-a/3)) I can't decide what to do from this or if i can do anything with what i found....

    • 2 years ago
  19. maheshmeghwal9 Group Title
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    ok np. :(

    • 2 years ago
  20. freckles Group Title
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    i'm still thinking :(

    • 2 years ago
  21. freckles Group Title
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    @KingGeorge any thoughts?

    • 2 years ago
  22. KingGeorge Group Title
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    Sorry for asking this, but just to clarify, you're asking for conditions under which a will be less than 0 correct?

    • 2 years ago
  23. freckles Group Title
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    What do you think about taking the contrapositive?

    • 2 years ago
  24. KingGeorge Group Title
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    If that's the question, looking at the derivative is a good idea. \[f(x)=x^3+ax+b\]\[f'(x)=3x^2+a\]If \(a\) is negative, then we would have 2 critical points that translate to local maxima and local minima. If a is positive, we would have 0 critical points.

    • 2 years ago
  25. KingGeorge Group Title
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    If we drew the graphs, \(a\) negative would look similar to this:|dw:1336193429080:dw|And \(a\) positive would look someting like|dw:1336193456467:dw|

    • 2 years ago
  26. KingGeorge Group Title
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    This means that if \(a\) were positive, then the function would always be increasing. Hence, we would only have one real root. But we're required to have all real roots. Contradiction! Therefore, a must be less than 0.

    • 2 years ago
  27. maheshmeghwal9 Group Title
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    thanx!

    • 2 years ago
  28. KingGeorge Group Title
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    You're welcome.

    • 2 years ago
  29. freckles Group Title
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    yes thanks george :)

    • 2 years ago
  30. maheshmeghwal9 Group Title
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    you both are good helper.

    • 2 years ago
  31. freckles Group Title
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    george is bester!

    • 2 years ago
  32. KingGeorge Group Title
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    Thank you guys :)

    • 2 years ago
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