Akar-akar persamaan kuadrat 2x²-5x+1=0 adalah X1 dan X2.Persamaan kuadrat baru yang akar akarnya(x1-1) dan (x2-1) adalah...

<p>Jawaban yang ebnar adalah D. <strong>2x² - x - 2 = 0</strong></p><p>&nbsp;</p><p>Pembahasan :</p><p>2x²-5x+1= 0</p><p>a = 2, b = -5 dan c = 1</p><p>x₁ + x₂ = -b/a</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 5/2</p><p>x₁ . x₂ = c/a</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 1/2</p><p>&nbsp;</p><p>(x₁ - 1) + (x₂ - 1) = x₁ - 1 + x₂ - 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = x₁ + x₂- 2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 5/2 - 2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 5/2 - 4/2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 1/2</p><p>(x₁ - 1) (x₂ - 1) = x₁ . x_2&nbsp; - x₁ - x₂ + 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= x₁ . x_2&nbsp; - (x₁ + x₂) + 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 1/2 - 5/2 + 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 1/2 - 5/2 + 2/2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= -2/2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= -1</p><p>&nbsp;</p><p>Persamaan kuadrat baru</p><p>x² - ((x₁ - 1) + (x₂ - 1)x + (x₁ - 1) (x₂ - 1) = 0</p><p>x² - 1/2 x - 1 = 0 &nbsp;(kalikan 2 untuk menghilangkan pecahan)</p><p><strong>2x² - x - 2 = 0</strong></p><p>&nbsp;</p>