If the roots of the equation ax2+bx+c=0  be in the ratio m:n  then

The given equation is ax2+bx+c=0 Given ratio of the roots are m:n Let the roots be mα and nα. then sum of the roots: mα+nα=  −  ba ⇒  (m+n)2α2=  b2a2    …… ( 1 )Product of the roots:  (mα)(nα)  =  ca   ⇒  mn  α2  =  ca     …… ( 2 )Dividing ( 1 ) by ( 2 ), we get  (m+n)2α2  mn  α2 =b2a2ca       ⇒(m+n)2ac  =b2  m n