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`

If the sum of the roots of x^(2) + bx + 1 = 0 , is equal to the sum of their squares, then b =

If the sum of the roots of the equation ax^2 +bx +c=0 is equal to sum of the squares of their reciprocals, then bc^2,ca^2 ,ab^2 are in

A real value of a, for which the sum of the roots of the equation x^(2)-2ax+2a-1=0 is equal to the sum of the square of its roots, is

If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in

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

The sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their recipocals, prove that (c)/(a),(a)/(b),(b)/(c) are in A.P.

If one root of the equation x^2+px+q=0 is the square of the other then

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

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 the roots of the equation x^(2)+px+q=0 is 3 times their difference, then