$a+b+c+d=0, ab+bc+cd+da+ac+bd=0, abc+abd+acd+bcd=k, abcd=-15$ $\frac{a+b+c}{d^2}=-\frac{1}{d}$ So we want to find equation with roots $-\frac{1}{a},-\frac{1}{b},-\frac{1}{c},-\frac{1}{d}$ $-15x^4-kx^3+1=0$ has roots $\frac{1}{a},\frac{1}{b},\frac{1}{c},\frac{1}{d}$ $-15x^4+kx^3+1=0$ has roots $-\frac{1}{a},-\frac{1}{b},-\frac{1}{c},-\frac{1}{d}$