BALTIC-WAY 2007 Problem 18

Let $a,b,c,d$ be non-zero integers, such that the only quadruple of integers $(x, y, z, t)$ satisfying the equation $$ax^2+by^2+cz^2+dt^2=0$$ is $x=y=z=t=0$ . Does it follow that the numbers $a,b,c,d$ have the same sign?