If `px^3 + qx^2 + rx+s=0` is a R.E. of second type then

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 x^(4) + px^(3) + rx + s^(2) is a perfect square then p^(3) + 8r =

If x^(4) + px^(3) + rx + s^(2) is a perfect square then ps =

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

find the condition that px^(3) + qx^(2) +rx +s=0 has exactly one real roots, where p ,q ,r,s,in R

find the condition that px^(3) + qx^(2) +rx +s=0 has exactly one real roots, where p ,q ,r,s,in R

For a cubic polynomial t(x) = px^(3) + qx^(2) + rx +s , which of the following is always true:

If x^4+px^3+qx^2+rx+5=0 has four positive roots,then the minimum value of pr is equal to

If the roots of x^(5) - 40 x^(4) + Px^(3) + Qx^(2) + Rx + S = 0 are in G.P. and sum of their reciprocals is 10, then |S| is equal to