[tex]\displaystyle\bf\\x^{2} +kx+3=0\\\\x_{2} =3x_{1} \ , \ x_{1} > 0 \\\\Teorema \ Vieta \ :\\\\x_{1} \cdot x_{2}=3\\\\x_{1} \cdot 3x_{1} =3\\\\3x_{1}^{2} =3\\\\x_{1}^{2} =1\\\\x_{1}=1 \ \ \ ; \ \ \ x_{2} =3\cdot 1=3\\\\Teorema \ Vieta \ :\\\\x_{1} +x_{2} =-k\\\\-k=1+3=4\\\\\boxed{k=-4}[/tex]