If the roots of a1x2 +b1x +c1=0 are m1,m2 and the roots of a2x2 +b2x +c2=0 are n1,n2 such that m1 n1 = m2n2 =1, thena) a1/ a2= b1/ b2= c1/ c2b) a1 a2= b1 b2= c1 c2c) a1/ c2= b1/ b2= c1/ a2

Dear Pooja,

correct option is c)

solution :

it is given that the roots of the two equations are reciprocals 

n1 =  1/ m1  and   n2 = 1/ m2

m1 and m2 are the roots of

a₁x² +b₁x +c₁=0 

m1 + m2 = -(b1/a1)          m1*m2= c1/a1

and n1 and n2 are roots of a₂x² +b₂x +c₂=0  -------1

n1+n2= 1/m1+1/m2 = (m1+m2)/(m1*m2)=-(b_1/c₁)  ----- sum of roots 

n1*n2=  1/(m1*m2)=a1/c1-----------product of roots

now we will form the equation as x² +(sum of roots)x +product of roots =0

x²   + (b_1/c₁₎ x +a1/c1 =0

multiply by c1 we get

c₁x²   + b₁x +a1 =0  -------2 this is same as the equation 1 now comparing we get

we get   c₁ = a_{2  ,}    b₁ = b₂    ,  a₁ = c₂

from this we get c1/a2 = 1        b1/b2= 1    a1/c2 =1   thus equating all three we get

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