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Homework Help: Sounds simple enough

  1. May 1, 2014 #1


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    1. The problem statement, all variables and given/known data

    I am asked to solve the following equation, giving answer in terms of k

    2. Relevant equations

    $$x^5 + k^2x = 0$$

    3. The attempt at a solution

    The answer is apparently 0. What is 0. Not even sure what that means.

    I would have thought: divide through by x to obtain

    $$k^2 = -x^4$$ →

    $$ k=x^2i $$ ???
  2. jcsd
  3. May 1, 2014 #2
    You solved for k. I think you were supposed to solve for x.

    I agree with you that there is more than one root.
    Last edited: May 1, 2014
  4. May 1, 2014 #3


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    Dividing both sides of an equation by anything except zero, gives you an equivalent equation.

    You can divide by x, as long as it's not equal to zero.
    What if x is zero?

    Evaluate that case another way, for instance, by plugging zero in for x.​
  5. May 1, 2014 #4


    Staff: Mentor

    The "answer" is not zero. Your answer should be in the form of equations that start with "x = ..."

    One of the solutions is x = 0, but there is another. Factoring the left side would be helpful.
  6. May 1, 2014 #5

    Ray Vickson

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    You have committed the worst sin in mathematics, viz., dividing by x before checking that it is allowed. If x = 0 you cannot do any such division---but in that case, you don't need to anyway. If x ≠ 0 then---and only then---can you divide both sides by x.
  7. May 2, 2014 #6


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    Thanks Mark & Ray for these lessons - a great help in learning to think properly.
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