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Math Help - range of values

  1. #1
    MHF Contributor
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    range of values

    Find the range of values of k if x^2+(k-3)x+k=0 has roots with the same sign .

    My working :
    x^2+(k-3)x+k=0
    let a and b be two roots of this equation .
    If both a and b were positive , (a+b)>0 , thus -k+3>0 , and 3>k
    Similarly ab> 0 , thus k>0

    If both a and b were negative , (a+b)<0 , thus -k+3<0 , then 3<k
    Similarly , ab>0 , thus k>0

    So the range of values should be 3>k , k>0 , and 3<k .
    But the answer given is k>0 only . So where is my mistake ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mathaddict View Post
    Find the range of values of k if x^2+(k-3)x+k=0 has roots with the same sign .

    My working :
    x^2+(k-3)x+k=0
    let a and b be two roots of this equation .
    If both a and b were positive , (a+b)>0 , thus -k+3>0 , and 3>k
    Similarly ab> 0 , thus k>0

    If both a and b were negative , (a+b)<0 , thus -k+3<0 , then 3<k
    Similarly , ab>0 , thus k>0

    So the range of values should be 3>k , k>0 , and 3<k .
    But the answer given is k>0 only . So where is my mistake ?
    Well suppose the result give is correct, then what happens when k=3 (the only point that your answer suggests the roots either don't exist or have different sign) ?

    The quadratic reduces to x^2+3=0 which has no real roots, so the given answer is obviously wrong at the only point it disagrees with yours.

    CB
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