Question

find condition that one root of the equation ax^2+bx+c =0 may be n times the othr

Answer 1

here , sum of root is
\[\alpha +\beta= -b/a\]

Answer 2

now ,
\[\alpha +n \alpha= -b/a\]

Answer 3

\[\alpha(1+n)=-b/a\]

Answer 4

so, \[\alpha= -b/a(1+n)\]

Answer 5

now, \[\alpha \beta=c/a\]

Answer 6

..........

Answer 7

\[\alpha ^{2}=c/na\]

Answer 8

so, condition is
n= ac/(b^2-ac)