What is the relationship between the two equations (the square of x) + PX + q = 0, Q * (the square of x) + p * x + 1 = 0

What is the relationship between the two equations (the square of x) + PX + q = 0, Q * (the square of x) + p * x + 1 = 0

x^2+px+q x1+x2=-p x1*x2=q
qX^2+pX+1=0 Xa+Xb=-p/q Xa*Xb=1/q
Xa+Xb=-p/q=(x1+x2)/(x1x2)=1/x2+1/x1
That is, two of the two equations are reciprocal to each other