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    the equation x^2+6x+10=0 has roots a and b

    find the quadratic equation with interger coeffiecients with roots a^3b and ab^3

    im stuck!! thanks alot
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    (Original post by sarah12345)
    the equation x^2+6x+10=0 has roots a and b
    no it doesnt have any roots, real roots anyway. possibly too hard for me
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    (Original post by sarah12345)
    the equation x^2+6x+10=0 has roots a and b

    find the quadratic equation with interger coeffiecients with roots a^3b and ab^3
    a + b = - 6

    ab = 10

    a^3 b + a b^3 = ab (a^2 + b^2) = ab ((a+b)^2 - 2ab) = (10)(36-20) = 160

    (a^3 b) (a b^3) = (ab)^4 = 10000

    Answer:

    x^2 - 160x + 10000
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    (Original post by RichE)
    a + b = - 6

    ab = 10

    a^3 b + a b^3 = ab (a^2 + b^2) = ab ((a+b)^2 - 2ab) = (10)(36-20) = 160

    (a^3 b) (a b^3) = (ab)^4 = 10000

    Answer:

    x^2 - 160x + 10000
    thanks

    do u know how you could do it by writting the roots in terms of another variable?
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    (Original post by sarah12345)
    do u know how you could do it by writting the roots in terms of another variable?
    not sure what you mean - can you expand on this?
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    well the way i tried to do it is to say that u=a^3b
    the rearange it to get u in terms of one of the roots and sub this into the equation but i got the wrong answer
    does that make any sence?
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    (Original post by sarah12345)
    well the way i tried to do it is to say that u=a^3b
    the rearange it to get u in terms of one of the roots and sub this into the equation but i got the wrong answer
    does that make any sence?
    you already have "u in terms of the roots" :confused:

    these questions are always the same and amount to writing symmetric expressions in a and b, in terms of the elementary symmetric polynomials a+b and ab
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    its how it says to do it in the book but your way works so ill leave it

    thanks alot
 
 
 
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