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Math Help - Using Vičte's Formula for a difficult quadratic problem

  1. #1
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    Using Vičte's Formula for a difficult quadratic problem

    Hi, with the problem:

    (a, c) and (b, d) are roots of the equations x^2 + ax - b = 0 and x^2 + cx + d = 0 respectively. Find a, b, c, d.

    Could this be solved with Vičte's Formula, or am I looking at this the wrong way?


    How would you solve it?

    BG
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  2. #2
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    You could equate coefficients and solve for a,b,c,d.

    (x-a)(x-c)=x^{2}+ax-b

    x^{2}-(a+c)x+ac=x^{2}+ax-b

    (x-b)(x-d)=x^{2}+cx+d

    x^{2}-(b+d)x+bd=x^{2}+cx+d

    -(c+a)=a, \;\ ca=-b, \;\ -(b+d)=c, \;\ bd=d
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