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    Hi I'm trying to solve the roots of x^2+5x+3=0 whose roots are 2α+ß and α+2ß.

    I've already solved the sum which is -15 but I'm having trouble with the product.

    I multiplied the roots to give me 2α^2 +5αß + 2ß^2 but now I don't know what to do for the α^2 and ß^2. how do I get the values for these?

    btw I know that αß=3 and α+ß= -5

    thanks
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    (Original post by HelloGoodbye)
    Hi I'm trying to solve the roots of x^2+5x+3=0 whose roots are 2α+ß and α+2ß.

    I've already solved the sum which is -15 but I'm having trouble with the product.

    I multiplied the roots to give me 2α^2 +5αß + 2ß^2 but now I don't know what to do for the α^2 and ß^2. how do I get the values for these?

    btw I know that αß=3 and α+ß= -5

    thanks
    Are you trying to find the new equation


    You need the standard result for (a+b)^2
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    (Original post by TenOfThem)
    Are you trying to find the new equation


    You need the standard result for (a+b)^2
    yes I am and so should I rearrange 2α^2 + 5αß +2ß^2 to 5αß + (α+ß)^2?

    thanks!
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    (Original post by HelloGoodbye)
    yes I am and so should I rearrange 2α^2 + 5αß +2ß^2 to 5αß + (α+ß)^2?

    thanks!
    No

    They are not the same

    You should know that (a+b)^2 = a^2+b^2+2ab
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    You could try expanding (x - (2a+b)) (x - (a+2b)) and comparing the results.


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    x2 - ax - 2bx - 2ax -bx + (2a+b)(a+2b)
    = x2 - 3ax -3bx + 2a2 + 5ab + 2b2

    So by comparing this to x2+5x+3 we get:

    -3ax-3bx = 5x
    a+b=-5/3

    2a2 + 5ab + 2b2 = 3

    Substitute or simultaneous to work out a and b

    edit: looking at your given answers I did something wrong here but it's late, I promise the method works :P
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    (Original post by TenOfThem)
    No

    They are not the same

    You should know that (a+b)^2 = a^2+b^2+2ab
    so does that mean I should substitute (α+β)^2 - 2αβ into the equation? I'm so confused!!
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    (Original post by HelloGoodbye)
    so does that mean I should substitute (α+β)^2 - 2αβ into the equation? I'm so confused!!
    Yes

    I don't know why you are confused

    This is a standard method ... It will be in your textbook and I would expect it to have been discussed in class
 
 
 
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