Tentukan akar-akar persamaan kuadrat berikut dengan menggunakan rumus abc.
- x² + 8x + 7 = 0 → x₁ = -1 atau x₂ = -7
- x² - 5x - 6 = 0 → x₁ = 6 atau x₂ = -1
- x² + 4x - 12 = 0 → x₁ = 2 atau x₂ = -6
- 2x² - x - 6 = 0 → x₁ = 2 atau x₂ = -³/₂
- 2x² - 7x -4 = 0 → x₁ = 4 atau x₂ = - ¹/₂
Penjelasan dan langkah-langkah
Diketahui:
Persamaan kuadrat:
- x² + 8x + 7 = 0
- x² - 5x - 6 = 0
- x² + 4x - 12 = 0
- 2x² - x - 6 = 0
- 2x² - 7x -4 = 0
Ditanyakan:
- Nilai akar-akar persamaan kuadrat dengan rumus abc = ?
Jawab:
- x² + 8x + 7 = 0
a = 1 b = 8 c = 7
[tex]x = \frac{-b\±\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-8\±\sqrt{8^2-4.1.7} }{2.1} \\\\x = \frac{-8\±\sqrt{64-28} }{2}\\\\x = \frac{-8\±\sqrt{36} }{2}\\\\x = \frac{-8\±6 }{2}[/tex]
x₁ = (-8 + 6 ) : 2 = - 1
x₂ = (-8 - 6 ) : 2 = - 7
- x² - 5x - 6 = 0
a = 1 b = -5 c = -6
[tex]x = \frac{-b\±\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-(-5)\±\sqrt{(-5)^2-4.1.-6} }{2.1} \\\\x = \frac{5\±\sqrt{25+24} }{2}\\\\x = \frac{5\±\sqrt{49} }{2}\\\\x = \frac{5\±7}{2}[/tex]
x₁ = (5 + 7 ) : 2 = 6
x₂ = (5 - 7 ) : 2 = -1
- x² + 4x - 12 = 0
a = 1 b = 4 c = 12
[tex]x = \frac{-b\±\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-4\±\sqrt{4^2-4.1.-12} }{2.1} \\\\x = \frac{-4\±\sqrt{16+48} }{2}\\\\x = \frac{-4\±\sqrt{64} }{2}\\\\x = \frac{-4\±8}{2}[/tex]
x₁ = (-4 + 8 ) : 2 = 2
x₂ = (-4 - 8 ) : 2 = - 6
- 2x² - x - 6 = 0
x = 2 b = -1 c = -6
[tex]x = \frac{-b\±\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-(-1)\±\sqrt{(-1)^2-4.2.(-6)} }{2.2} \\\\x = \frac{1\±\sqrt{1+48} }{4}\\\\x = \frac{1\±\sqrt{49} }{4}\\\\x = \frac{1\±7}{4}[/tex]
x₁ = (1 + 7 ) : 4 = 2
x₂ = (1 - 7 ) : 4 = - 6/4 = -3/2
- 2x² - 7x -4 = 0
a = 2 b = -7 c = -4
[tex]x = \frac{-b\±\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-(-7)\±\sqrt{(-7)^2-4.2.(-4)} }{2.2} \\\\x = \frac{7\±\sqrt{49+32} }{4}\\\\x = \frac{7\±\sqrt{81} }{4}\\\\x = \frac{7\±9}{4}[/tex]
x₁ = (7 + 9 ) : 4 = 4
x₂ = (7 - 9) : 4 = - -2/4 = -1/2
Pelajari lebih lanjut
Materi tentang menentukan akar-akar kuadrat dengan rumus abc https://brainly.co.id/tugas/5283878
#BelajarBersamaBrainly #SPJ1
[answer.2.content]
