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Homework Help: Quadratic equation problem.

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    How should be the value of a so quadratic equation [tex]ax^2-4x+4=0[/tex] to have double solutions?
    [tex]A)\;\;2[/tex]
    [tex]B)\;\;1[/tex]
    [tex]C)\;-1[/tex]
    [tex]D)\;-2[/tex]
    2. Relevant equations



    3. The attempt at a solution
    [tex]D=b^2-4ac[/tex]
    If:
    [tex]D>0\;\;\rightarrow\; {x_1,x_2}\;\rightarrow\;\text{double solutions.}[/tex]
    [tex]D=0\;\;\rightarrow\; {x_1}\;\rightarrow\;\text{only one solution}[/tex]
    [tex]D<0\;\;\rightarrow\; \text{no solution.}[/tex]

    so:
    [tex](-4)^2-4*a*4=16-16*a[/tex]
    [tex]\text{If:}\;\;a=-1\;\;\rightarrow\;D=32[/tex]
    [tex]\text{If:}\;\;a=-2\;\;\rightarrow\;D=48[/tex]

    Which one should be?? thank you.
     
  2. jcsd
  3. Jan 16, 2012 #2
    Looks like both C and D work. Are you only allowed to choose one answer?
     
  4. Jan 16, 2012 #3

    "Double" here should mean the solutions are twins.


    So, you need D = 0, so that there is a repeated solution.

    [itex]So, \ set \ \ 16 - 16a \ \ equal \ to \ 0 \ and \ solve [/itex]

    [itex]\ for \ that \ value \ of \ a.[/itex]


    *** Edit


    That means that a = 1.

    So, the answer is B.



    ***2nd edit:

    Curious3141 repeated the essence of what I already stated.
     
    Last edited: Jan 16, 2012
  5. Jan 16, 2012 #4

    Curious3141

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    Terrible question. "Double solutions" is nonsensical. It's either "distinct real roots" for D>0 or "single repeated root" for D=0.
     
  6. Jan 16, 2012 #5
    No, by double, I meant: example: [tex]x_1=3\;\;,\;\;x_2=7[/tex] just example, not twins or the same but two different, sorry for that.

    "Terrible question??" let's see if you understand it in my Language.!!

    Sa duhet të jetë parametri a ashtuqë ekuacioni [tex]ax^2-4a+4=0 [/tex] te kete dy zgjidhje te ndryshme?

    Do you like that??... English is a FOREIGN language for me, and I'm not blaming you for anything, It's ok that you defined it "Terrible question" , but try to understand (ask me) before you judge! So I guess, C and D should be correct, am I wrong?
     
  7. Jan 16, 2012 #6

    Curious3141

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    No need to get all grumpy. I was commenting on the question as it was phrased, and I naturally assumed that was how it had been presented to you. How was I supposed to know you had translated it in an ambiguous fashion? I am not a mindreader.:rolleyes:

    In any case, if you meant TWO separate real roots, there is no unique answer, as LearninDaMath has already pointed out to you. C and D both fit.
     
  8. Jan 16, 2012 #7
    Kreshnik , here double roots means "real and distinct roots."
    Here discriminant is greater than 0.

    D>0
    You have

    D=b2−4ac
    or
    b2−4ac > 0
    Plug in the values and find for a i.e. inequality in "a".
    What do you get ?
     
  9. Jan 16, 2012 #8

    ehild

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    Sankaplmittal,

    double roots mean that the roots are equal. http://www.tpub.com/math1/17g.htm
    Kreshnik has shown already at what values of parameter "a" the discriminant is greater than zero, so the equation has two real and distinct roots .

    ehild
     
  10. Jan 16, 2012 #9
    Curious3141 I hope I didn't offend you, if I did it, I'm sorry.
    Thanks everyone for being patience. I think now I learnt what I wanted to know.
    Thank you everyone.
     
  11. Jan 16, 2012 #10

    Curious3141

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    No worries, didn't mean to offend you either, and glad you learned what you wanted to know. :smile:
     
  12. Jan 16, 2012 #11

    Mark44

    Staff: Mentor

    Out of curiosity, what language is this? Hungarian?
     
  13. Jan 16, 2012 #12

    I never encountered a problem where I had to choose a number that produced two identical roots. I've only had to show whether there were two real, two complex, or 1 roots. I saw this question and thought i'd try my best to be productive by contributing while patiently waiting for my most recent thread to garner a little help lol.
     
  14. Jan 16, 2012 #13

    SammyS

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    If you're referring to a quadratic equation, then the case of "1 roots" is the same as the case of two identical real roots .
     
  15. Jan 16, 2012 #14
    Oh, so asking for "double solutions" or "two identical solutions" is the same thing as asking for 1 solution? If so, then of course, makes sense. Is it common for the x that yields 1 root to be asked in the terminology of finding "two identical solutions?" I don't recall hearing it put like that before.
     
  16. Jan 16, 2012 #15

    ehild

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    No, it is not. :smile:

    But Google said it was Albanian, and "te kete dy zgjidhje te ndryshme" = "Have two different solutions"

    Is it right, Kreshnik?

    ehild
     
  17. Jan 18, 2012 #16
    Exactly...I hope you're convinced now. I'm albanian, Kosova.
    Cheers!
     
  18. Jan 18, 2012 #17

    Bacle2

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    Mark44 wrote:

    "Out of curiosity, what language is this? Hungarian? "

    I think the value of the roots is the same in any language ;) .
     
  19. Jan 19, 2012 #18

    ehild

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    So we live quite close -I am Hungarian. :smile:

    ehild
     
  20. Jan 19, 2012 #19
    I guess we do! I'm glad we're neighbour. Take care. :smile:
     
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