For what values of p and q, the expression, `x^(4) - 14x^(3) + 71x^(2) + px + q` is a perfect square ?

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

Find the values of p and q so that x^(4)+px^(3)+2x^(2)-3x+q is divisible by (x^(2)-1)

Under what condition on p and q, one of the roots of the equation x^(2) + px + q = 0 is the square of the other?

If p and q are the roots of x^2 + px + q = 0 , then find p.

If (x-3) is the HCF of x^(3) - 2x^(2) +px + 6 and x^(2) - 5x +q, find 6p +5q

What are the values of p and q respectively, if (x-1) and ( x+ 2) divide the polynomial x^(3) + 4x^(2)+ px +q ?