Let and be the roots of the quadratic equation a x^2+b x+c=0 . Observe the lists given below The correct match of List-I from List-II is (i) (ii) (iii) (iv)

Step-by-step solution

Using the condition that the roots of a x^2+b x+c=0 may be in the ratio m: n is m n b^2=a c(m+n)^2 . (i) If the roots are = , then aligned b^2 & =a c( + )^2 b^2 & =4 a c aligned aligned & b^2=4 a c & (ii) If the roots are =2 , then & & 2 b^2=a c( +2 )^2 & 2 b^2=9 a c aligned (iii) If the roots are =3 , then aligned 3 b^2 & =a c( +3 )^2 3 b^2 & =16 a c aligned (iv) If the roots are = ^2 , then aligned & (a^2 c )^ 1 2+1 + (a c^2 )^ 1 2+1 =-b & (a^2 c )^ 1 3 + (a c^2 )^ 1 3 =-b aligned Hence, option (d) is correct.