The solutions of y^2+by+c=0 are the reciprocals of the solutions of x^2-7x+12=0. Find the value of b+c?

1 Answer
Mar 7, 2017

b+c=-1/2

Explanation:

(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1x_2
(y-1/x_1)(y-1/x_2) = y^2-(x_1+x_2)/(x_1x_2)y+1/(x_1x_2)

so we have

12c=(x_1x_2)/(x_1x_2)=1->c=1/12

and x_(1,2) = (7pm sqrt(49-48))/2={3,4} so

b=-(3+4)/12=-7/12 and finally

b+c=-1/2