The cubic equation whose roots are the squares of the roots of x^3-2 x^2+10 x-8=0 , is

Step-by-step solution

Let, , and are the roots of aligned & x^3-2 x^2+10 x-8 & =0 & + + & =2, aligned + + =10 and =8 Now, ^2+ ^2+ ^2 aligned & =( + + )^2-2( + + ) & =(2)^2-2(10)=-16 aligned aligned ^2 ^2+ & ^2 ^2+ ^2 ^2 & =( + + )^2-2( + + )( ) & =(10)^2-2(2)(8) & =100-32=68 aligned and ^2 ^2 ^2=(8)^2=64 Required cubic equation is aligned & x^3- ( ^2+ ^2+ ^2 ) x^2+ ( ^2 ^2+ ^2 ^2+ ^2 ^2 ) x & - ^2 ^2 ^2=0 & x^3-(-16) x^2+(68) x-64=0 & x^2+16 x^2+68 x-64=0 aligned