If the sum of two roots of the equation ` x^4 +px^3 +qx^2 + rx +s=0` equals the sum of the other two ,prove that `p^3 + 8r =4pq`

Prove that the sum of any two of the roots of the equation x^4 +px^3 +qx^2 +rx +s =0 is equal to the sum of the remaining two roots of the equation iff p^3 -4pq +8r =0

If the sum of two roots of the equation x^(3) -2px^(2)+3qx -4r=0 is zero, then the value of r is

Solve the equation x^4 -2x^3 + 4x^2 + 6x -21=0 the sum of two of roots being zero.

IF 3+ 4i is a root of the equation x^2 +px +q=0 then

If one root of x^(3) + 3x^(2) + 5x + k = 0 may be the sum of the other two roots then k =

If the sum of two of the roots of x^(4) - 2x^(3) - 3x^(2) + 10x - 10 = 0 is zero then the roots are