The roots and of a quadratic equation, satisfy the relations + = ^2+ ^2 and = ^2 ^2 . What is the number of such quadratic equations?

Step-by-step solution

aligned & = ^2 ^2 (1- )=0 & =0 or 1 aligned When =1 then = 1 aligned & Again from + = ^2+ ^2 & 1 + = 1 ^2 + ^2 ^2- = 1 - 1 ^2 & ( -1)= ( -1) ^2 ( -1) ( - 1 ^2 )=0 aligned aligned & ( -1) ( ^3-1 )=0 ( -1)^2 ( ^2+ +1 )=0 & =1 and = -1 3 i 2 aligned Again, when =1 , then = 1 =1 , roots ( , )=(1,1) When = -1+ 3 i 2 , then = -1- 3 i 2 Roots ( , )= ( -1 3 i 2 , -1 3 i 2 ) Thus, number of different quadratic equations =2 .