If the sum of the rotsof the equation `px^2+qx+r=0` be equal to the sum of their squares, show that `2pr=pq+q^2`

The sum of the roots of the equation x^2+ px + q= 0 is equal to the sum of their squares, then

The sum of the roots of the equation x^(2) + px + q = 0 is equal to the sum of their squares, then :

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

If the sum of the roots of the equation x^2-px+q=0 be three times their difference show that, 2p^2=9q .

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

If the roots of the equation px^(2)+qx+r=0(pne0) be equal, then q=2sqrt(pr) .

If the sum of the two roots of x^3 +px^2 +qx +r=0 is zero then pq=

If the sum of the two roots of x^3 +px^2 +qx +r=0 is zero then pq=

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

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