Tentukanlah rentang k sehingga penyelesaian persamaan kuadrat x²-(k+1)x+4k-5= 0, yaitu α dan β , memenuhi -2<α< -1 dan 2<β<3.
Answer (3)
The process of accumulating capital is called investment. Investment can be done in various categories like land, labor and capital. Investment in land does not mean investing only in the lands that are cultivated or where buildings can be built. It can also include land where natural resources are available. Capitals can be machinery, buildings, raw materials and several other things. Labor will include people giving physical labor as well as those people that use their intelligence. So brain and physical labor are both investments.
The process of accumulating capital is called investment, which involves allocating resources to generate returns or build up capital for economic activities. This process can include physical, human, and natural capital and plays a crucial role in business growth and economic development. Therefore, the correct option is C. investment.
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Jawaban:[tex] - \frac{1}{4} < k < \frac{3}{4} [/tex]Penjelasan dengan langkah-langkah:Diberikan persamaan kuadrat:x^2 - (k+1)x + 4k - 5 = 0 dan diberi syarat:[tex] - 2 < \alpha < - 1 \: dan \: 2 < \beta < 3[/tex]---### **Langkah 1: Hubungan antara akar dan koefisien**Dari bentuk umum persamaan kuadrat:x^2 - (k+1)x + (4k - 5) = 0maka:* Jumlah akar: alpha + beta = k+1* Hasil kali akar: alpha beta = 4k - 5---### **Langkah 2: Batasan jumlah akar**Karena [tex]2 < \alpha < - 1 \: dan \: 2 < \beta < 3[/tex], kita cari batas-batas dari alpha + beta* Batas bawah: -2 + 2 = 0* Batas atas: -1 + 3 = 2Jadi:[tex]0 < \alpha + \beta < 2 \: = > 0 < k + 1 < 2 = > - 1 < k < 1[/tex]---### **Langkah 3: Batasan hasil kali akar*** Batas bawah: [tex] \alpha \beta > - 2 \times 3 = - 6[/tex]* Batas atas: [tex] \alpha \beta < - 1 \times 2 = - 2[/tex]Jadi:[tex] - 6 < \alpha \beta < - 2 \: \: = > \: \: - 6 < 4k - 5 < - 2[/tex]Selesaikan pertidaksamaan ini:1. Tambah 5:[tex] - 1 < 4k < 3[/tex]2. bagi 4[tex] - \frac{1}{4} < k < \frac{3}{4} [/tex]---### **Langkah 4: Irisan interval**Dari langkah 2: -1 < k < 1Dari langkah 3: [tex] - \frac{1}{4} < k < \frac{3}{4} [/tex]Ambil irisan dari keduanya:[tex] - \frac{1}{4} < k < \frac{3}{4} [/tex]✅ **Jawaban akhir:**[tex] - \frac{1}{4} < k \: < \frac{3}{4} [/tex]
