Question

Find the condition that the ratio between the roots of the equation ax*2+bx+c=0 may be m:n

Answer 1

Given AX^2+BX+C=0
ROOTS ARE IN RATIO M:N.
LET THE ROOTS BE MY AND NY
SUM OF ROOTS =MY+NY=Y(M+N)=-B/A
Y=-B/A(M+N)
PRODUCT OF ROOTS=MNY^2=C/A
MN*{-B/A(M+N)}^2=C/A
MNB^2=CA^2(M+N)^2/A=CA(M+N)^2