# Using Viète's Formula for a difficult quadratic problem

• September 8th 2009, 08:06 AM
BG5965
Using Viète'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 Viète's Formula, or am I looking at this the wrong way?

How would you solve it?

BG
• September 8th 2009, 08:56 AM
galactus
You could equate coefficients and solve for a,b,c,d.

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

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

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

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

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