Consider the following statements in respect of the given equation : (x^2+2 )^2+8 x^2=6 x (x^2+2 ) 1. All the roots of the equation are complex. 2. The sum of all the roots of the equation is 6 . Which of the above statements is/are correct?

Step-by-step solution

aligned & (x^2+2 )^2+8 x^2=6 x (x^2+2 ) & Let x^2+2=y & y^2+8 x^2=6 x y & y^2-6 x y+8 x^2=0 & y= 6 x 36 x^2-32 x^2 2 aligned aligned & y= 6 x 2 x 2 =3 x x & y=4 x, 2 x & At y=4 x & x^2+2=4 x & x^2-4 x+2=0 aligned Discriminant, D =16-8=8 0 Roots are real. Sum of roots =-(-4)=4 aligned & At x=2 x & x^2+2=2 x & x^2-2 x+2=0 & D=4-8=-4 0 aligned Roots are complex. Sum of roots =2 Sum of all roots =4+2=6 only statement 2 is correct. Correct option is (B)