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Math Help - completing the square

  1. #1
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    completing the square

    Hi everyone

    could you please help me answer these two questions? Thanks! x

    1. Show that there is no real value of the constant c for which the equation

    cx^2 + (4c+1)x + (c+2) = 0

    2. Given that the roots of the equation x^2+ax+(a+2) = 0 differ by 2, find the possible values of the constant a. Hence state the possible values of the roots of the equation.
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  2. #2
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    Quote Originally Posted by emsypooh View Post
    2. Given that the roots of the equation x^2+ax+(a+2) = 0 differ by 2, find the possible values of the constant a. Hence state the possible values of the roots of the equation.
    Hi

    Let x_1 and x_2 the solutions of the equation x+ax+(a+2) = 0

    What relations can you write involving x_1 and x_2 ?
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  3. #3
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    Quote Originally Posted by running-gag View Post
    Hi

    Let x_1 and x_2 the solutions of the equation x+ax+(a+2) = 0

    What relations can you write involving x_1 and x_2 ?
    Hi there

    I'm sorry, i sound so stupid, but i really don't know
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  4. #4
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    The first one is of course x_1 - x_2 = 2 since you know that the roots differ by 2

    Now you should also be able to write x_1 + x_2 = ... and x_1 \times x_2 = ...

    You should have learned this I suppose
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  5. #5
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    nopeee, we havent learnt any of this. we went from factorizing to this.

    so the answers are x1+x2 and x1 (times) x2?

    sorry about this..
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  6. #6
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    Okay
    Since x_1 and x_2 are the roots of x+ax+(a+2) you can write
    x^2+ax+(a+2) = (x-x_1)(x-x_2)

    Expanding the RHS x^2+ax+(a+2) = x^2-(x_1+x_2)x + x_1 x_2

    Therefore
    x_1 + x_2 =-a
    and
    x_1 x_2 = a+2

    Now you know x_1 + x_2 =-a and x_1 - x_2 =2

    That will give you x_1 and x_2 with respect to a
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  7. #7
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    Quote Originally Posted by running-gag View Post
    Okay
    Since x_1 and x_2 are the roots of x+ax+(a+2) you can write
    x^2+ax+(a+2) = (x-x_1)(x-x_2)

    Expanding the RHS x^2+ax+(a+2) = x^2-(x_1+x_2)x + x_1 x_2

    Therefore
    x_1 + x_2 =-a
    and
    x_1 x_2 = a+2

    Now you know x_1 + x_2 =-a and x_1 - x_2 =2

    That will give you x_1 and x_2 with respect to a
    thank you so, so, so, so much!!!! i really, really appreciate it

    do you know how to work out the other question too? x
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  8. #8
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    Quote Originally Posted by emsypooh View Post
    thank you so, so, so, so much!!!! i really, really appreciate it

    do you know how to work out the other question too? x
    This one is not finished !
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  9. #9
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    Quote Originally Posted by running-gag View Post
    This one is not finished !

    oh yeah whoops!

    the full question is,

    show that there is no real value of the constance c for which the equation

    cx^2 + (4c+1)x + (c+2) = 0

    has a repeated root.

    whoops!
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  10. #10
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    No

    I mean the second exercise is not yet finished
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  11. #11
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    aahhhh okay, i understand
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