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Thread: Using Viète's Formula for a difficult quadratic problem

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

    Hi, with the problem:

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

    Could this be solved with Viète'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.

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

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

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

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

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