The condition
`f(x)=x^3 + px^2 + qx +r ( x in R)` to have no extreme value is

The condition for f(x) =x^3+px^2+qx+r^',x in R) to have no extreme value , is

The condition that the x^(3) -px^(2) + qx -r = 0 may be the sum of the other two roots is zero =

Find the condition that the equation x^3 - px^2 + qx -x = 0 should have its roots in G.P.

Find the condition that the zeroes of the polynomial f(x) = x^3 – px^2 + qx - r may be in arithmetic progression.

Find the condition which must be satisfied by the zeros of f(x) = x^(3) - px^(2) + qx - r , when the sum of its two zeros is zero .

The condition that the roots of x^3 +3 px^2 +3qx +r = 0 may be in H.P. is

The condition that the roots of x^(3) + 3px^(2) + 3qx + r = 0 may be in G.P is

find the condition that x^3 -px^2 +qx -r=0 may have two roots equal in magniude but of opposite sign