The condition that a root of the equation may be reciprocal to a root of is
Possible Answers
Possible Answer
Hello, swordfish774!
. . . . Are they kidding?
.[1]
. . .[2]
Equating [1] and [2], we have: .
Multiply (a) and (b): .
Multiply (b) and (c): .
Multiply (a) and (c): .
Square (f): .
Multiply (e) and (d):. .
Therefore, (g) = (h): .
This reminds me of a similar question: If p and q are rhe roots of ax^2+bx+c=0 find the equation whose roots are 1/p and 1/q
We have p+q=-b/a and pq=c/a So 1/p+1/q=(q+p)/pq=(-b/a)/(c/a)=-b/c and (1/p)*(1/q)=1/pq=a/c
So required equation is x^2+(b/c)x+(a/c)=0 That is cx^2+bx+a=0