If , and are the roots of the equation x^3+a^2+b x+c=0 , then the roots of the equation x^3+ (2 b-a^2 ) x^2+ (b^2-2 a c ) x-c^2=0 are

Step-by-step solution

, and are roots of x^3+a^2+b x+c=0 + + =-a a=-( + + ) aligned & + + =b & =-c c=- aligned Let ^ , ^ and ^ are the roots of the equation ^ + ^ + ^ =( + + )^2-2( + + ) ^ + ^ + ^ = ^2+ ^2+ ^2 ...(i) And ^ ^ + ^ ^ + ^ ^ =b^2-2 a c aligned & ^ ^ + ^ ^ + ^ ^ =( + + )^2-2( ) & ^ ^ + ^ ^ + ^ ^ =( )^2+( )^2+ ^2 ^2 aligned = ^2 ^2+ ^2 ^2+ ^2 ^2 ...(ii) And ^ ^ ^ =- (-c^2 )=c^2= ^2 ^2 ^2 ... (iii) from eqs. (i), (ii) & (iii) ^ = ^2, ^ = ^2, ^ = ^2 Roots are ^2, ^2 and ^2