Viete's Theorem vs MGMAT factoring approach: +/- b?

Question

Hi together,

while taking note of tips and tricks across the posts I stumbled across the following issue in dealing with quadratic equations ( ax^2+bx+c =0 , assuming a is not 0):

A) MGMAT Approach to factoring a quadratic equation 
First divide by a. Then, get to  (x+U)(x+V) = 0  by making sure that
 U + V = b  ( -> positive b ) and 
 U * V = c .

B) Viete's formula 
Quoted from Bunuel (Unfortunately, I can't link to it directly as this is my first post):

"Viete's formula for the roots x1 and x2 of equation  (ax^2+bx+c=0) :

x1+x2=−b/a    (-> Here -b is used )
AND  x1∗x2=c/a "

Does anyone know why one approach uses b and the other -b as the sum of the roots?

Thanks already in advance!

Best

Kinshook · Answer

hi  Abcse

(ax^2+bx+c=0) 
 (x^2+bx/a+c/a=0) 
 (x+U)(x+V) = 0 
Roots of the equation = {x1,x2} or {-U,-V}
In this approach, roots are -U & -V and in another approach, roots are x1 & x2.
x1 + x2 = - b/a = - (U+V)

Hope it is clear now.

Kinshook · Answer

ax^2+bx+c = a(x-x1)(x-x2) = a(x+U)(x+V) = 0
x1 + x2 = - b/a = -(U+V)

bumpbot · Answer

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Viete's Theorem vs MGMAT factoring approach: +/- b?

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