show that the equation $x^5+5px^3+5p^2x+q=0$ will have a pair of equal roots, if $q^2+4p^5=0$ how can I show that the equation $x^5+5px^3+5p^2x+q=0$ will have a pair of equal roots, if $q^2+4p^5=0$.
can anyone help me.thanks a lot.

The discriminant vanishes iff there are common roots of the polynomial. In this case the discriminant is $3125(4p^2+q^2)^2$.
