[tex]\displaystyle\bf\\x^{2} +px+q=0\\\\x_{1} + x_{2} =12\\\\x_{1} \cdot x_{2} =-24\\\\Teorema \ Vieta \ :\\x_{1} + x_{2} =-p \ \ \ \Rightarrow \ \ \ -p=12 \ \ \Rightarrow \ \ \ p=-12\\\\x_{1} \cdot x_{2} =q \ \ \ \ \ \ \ \Rightarrow \ \ \ \ \ q=-24\\\\\\\boxed{x^{2} -12x-24=0}[/tex]