Question

if alpha and beta are the zeroes of the polynomial x2+5x+5, find the value of alpha^-1 +beta^-1

Answer 1

a=1, b=5 and c=5

we know, alpha+beta= -b/a = -5/1 = -5

Also, alpha × beta = c/a = 5/1 =5

A.T.Q:- alpha^-1 +beta^-1 = 1/alpha + 1/beta

After taking LCM, we get :

(alpha+beta) ÷ (alpha×beta) = -5÷5 = -1