Question

if alpha and beta are the roots of education ax^+bx+c=0 find the value of alpha/beta+beta/alpha

Answer 1

Heya !!!



P(X) = AX² + BX + C


Here,



Coefficient of X² = A


Coefficient of X = B

And,


Constant term = C




Sum of zeroes = -( Coefficient of X)/Coefficient of X²




Alpha + Beta = -B/A



And,


Product of zeroes = Constant term/Coefficient of X².


Alpha × Beta = C/A




Now,



Alpha / Beta + Beta / Alpha = (Alpha+ẞ/Alphaß)




=> -B/A / C/A



=> -B/C

Hence,


Alpha + Beta / Alpha × Beta = -B/C



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