Sebuah persamaan kuadrat berbentuk x^2-2px+p+12=0. Persamaan kuadrat tsb mempunyai 2 akar yg tandanya berbeda apabila...

Persamaan kuadrat tsb mempunyai 2 akar yg tandanya berbeda apabila D > 0

[tex]\displaystyle \text{Apabila berbeda tanda, maka}\\D\ \textgreater \ 0\\b^2-4ac\ \textgreater \ 0\\(-2p)^2-4(1)(p+12)\ \textgreater \ 0\\4p^2-4(p+12)\ \textgreater \ 0\\p^2-p-12\ \textgreater \ 0\\(p-4)(p+3)\ \textgreater \ 0\\p\ \textless \ -3\vee p\ \textgreater \ 4...\text{HP}_1\\\\x_1x_2\ \textless \ 0\\\frac ca\ \textless \ 0\\\frac{p+12}{1}\ \textless \ 0\\p\ \textless \ -12...\text{HP}_2\\\\\text{HP}=\text{HP}_1\cap\text{HP}_2\\\boxed{\boxed{\text{HP}=\{p|p\ \textless \ -12,p\in\mathbb{R}\}}}[/tex]