Lanjutan Materi Pertidaksamaan Berkaitan Materi Pertidaksamaan Kuadrat

 Sebelumya 

silahkan buka di sini

A. PERTIDAKSAMAAN KUADRAT

$\begin{array}{ll}\\ &\underline{\textbf{Bentuk Umum}}:\\\\ &\color{blue}\begin{cases} ax^{2}+bx+c< 0 \\ ax^{2}+bx+c\leq 0 \\ ax^{2}+bx+c > 0 \\ ax^{2}+bx+c \geq 0 \end{cases}\\ & \end{array}$

B. PENYELESAIAN PERTIDAKSAMAAN KUADRAT

$\begin{aligned}&\\ ax^{2}+bx+c\: \: ...\: \: 0&\\ \color{blue}\textrm{diubah menjadi}&\quad \: ax^{2}+bx+c=0\\ &\Leftrightarrow a\left ( x-x_{1} \right )\left ( x-x_{2} \right )=0\\ &\Leftrightarrow x=x_{1}\quad \textrm{atau}\quad x=x_{2}\\ &\end{aligned}$

$\begin{array}{|l|c|}\hline \textrm{Pertidaksamaan}&\textrm{Himpunan Penyelesaian dengan}\: \:x_{1}<x_{2} \\\hline ax^{2}+bx+c< 0&\left \{ x|x_{1}<x<x_{2},\: x\in \mathbb{R} \right \} \\\hline ax^{2}+bx+c\leq 0&\left \{ x|x_{1}\leq x\leq x_{2},\: x\in \mathbb{R} \right \} \\\hline ax^{2}+bx+c> 0&\left \{ x|x<x_{1}\: \: \textrm{atau}\: \: x>x_{2},\: x\in \mathbb{R} \right \} \\\hline ax^{2}+bx+c\geq 0&\left \{ x|x\leq x_{1}\: \: \textrm{atau}\: \: x\geq x_{2},\: x\in \mathbb{R} \right \} \\\hline \end{array}$

$\color{blue}\LARGE\fbox{CONTOH SOAL}$

$\begin{array}{ll}\\ &\textrm{Tentukan himpunan penyelesaian \textbf{PtKSV}}\\ &\textrm{(Pertidaksamaan Linear Satu Variabel) berikut ini!}\\ &\textrm{a}.\quad x^{2}-6x+8< 0\\ &\textrm{b}.\quad x^{2}-6x+8\leq 0\\ &\textrm{c}.\quad x^{2}-6x+8> 0\\ &\textrm{d}.\quad x^{2}-6x+8\geq 0\\\\ &\textrm{Jawab}:\\ \end{array}$

$\begin{aligned}&\\ x^{2}-6x+8\: \: ...\: \: 0&\\ \color{blue}\textrm{diubah menjadi}&\quad \: x^{2}-6x+8=0\\ &\Leftrightarrow 1\left ( x-2 \right )\left ( x-4 \right )=0\\ &\Leftrightarrow x=2\quad \textrm{atau}\quad x=4\\ &\end{aligned}$