if the roots of a1x2+b1x+c1=0 are alpha ,beta and that of a2x2+b2x+c2=0 are gamma and delta such that alpha*gamma=beta*delta - Maths - Logs Equations and Inequalities

Question

if the roots of
a1x2+b1x+c1=0 are alpha
,beta and that of
a​2x2+b2x+c2=0
are gamma and delta such that alpha*gamma=beta*delta =1,then
a
a1/a2=b1/b2=c1/c2

b
a1/c2=b1/b2=c1/a2

c
a1a2=b1b2=c1c2

d none of these

Rahul Raj · Accepted Answer

Dear student

a1x2+b1x+c1=0α+β=-b1a1 αβ=c1a1a2x2+b2x+c2=0γ+δ=-b2a2 γδ=c2a2αγ=βδ=1αβγδ=(αγ)(βδ)=1*1=1αβγδ=αβγδ=c1a1c2a2=1so, c1a1c2a2=1c1a2=a1c2α+β=-b1a11γ+1δ=-b1a1γ+δγδ=-b1a1-b2a2c2a2==-b1a1b2c2=b1a1b1b2=a1c2and from abovec1a2=a1c2option B

Regards

if the roots of a1x2+b1x+c1=0 are alpha ,beta and that of a​2x2+b2x+c2=0 are gamma and delta such that alpha*gamma=beta*delta =1,then a.a1/a2=b1/b2=c1/c2 b.a1/c2=b1/b2=c1/a2 c.a1a2=b1b2=c1c2 d.none of these

if the roots of a₁x²+b₁x+c₁=0 are alpha ,beta and that of a₂x²+b₂x+c₂=0 are gamma and delta such that alphagamma=betadelta =1,then
a.a₁/a₂=b₁/b₂=c₁/c₂
b.a₁/c₂=b₁/b₂=c₁/a₂
c.a₁a₂=b₁b₂=c₁c₂
d.none of these