2x²+5x-12=0
akar akar nya 2x¹ dan 2x²
tong dijawab secepat nya
x² + 5x - 24 = 0
Penjelasan dengan langkah-langkah:
2x²+5x-12=0
a = 2, b = 5, c = -12
x1 + x2 = -b/a = -5/2
x1 . x2 = c/a = -12/2 = -6
persamaan baru dengan akar akar 2x1 dan 2x2
2x1 + 2x2 = 2 (x1 + x2) = 2 x (-5/2) = -5
2x1 . 2x2 = 4x1.x2 = 4 x -6 = -24
persamaan barunya
x² - (2x1 + 2x2) + (2x1.2x2) = 0
x² - (-5)x + (-24) = 0
x² + 5x - 24 = 0
Jawaban:
x² + 5x - 24 = 0
Penjelasan dengan langkah-langkah:
Menentukan pers. kuadrat baru.
–—
2x² + 5x - 12 = 0
tntukan akar-akar dgn rumus abc
x₁,₂ = -b ± √b² - 4ac / 2a
x₁,₂ = -5 ± √(5² - 4(2)(-12)) / 2(2)
x₁,₂ = -5 ± √(25 + 96) / 4
x₁,₂ = -5 ± √121 / 4
x₁,₂ = -5 ± 11 / 4
x₁ = -5 + 11 / 4 = 6/4 = 3/2
x₂ = -5 - 11 / 4 = -16/4 = -4
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Akar² prs. kuadrat baru
x₁ = 2x₁ = 2(3/2) = 3
x₂ = 2x₂ = 2(-4) = -8
Maka, pers. kuadrat barunya adalah:
x₁ = 3 V x₂ = -8
x₁ - 3 = 0 V x₂ + 8 = 0
(x - 3) (x + 8) = 0
x² + 5x - 24 = 0
–—
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