diketahui X1 X2 dan X3 adalah akar-akar persamaan suku banyak x³ - 8x² + 9x + n = 0 Jika X1 = 2 X2 tentukan nilai n

Jawaban yang benar adalah 18 Ingat konsep berikut ini: ax³ + bx² + cx + d = 0 x1 + x2 + x3 = -b/a x1x2 + x1x3 + x2x3 = c/a x1 ⋅ x2 ⋅ x3 = -d/a x³ - 8x² + 9x + n = 0 x1 = 2 x2 misal: x2 = p x1 + x2 + x3 = -b/a x1 + x2 + x3 = -(-8)/1 x1 + x2 + x3 = 8 2p + p + x3 = 8 3p + x3 = 8 x3 = 8 - 3p x1x2 + x1x3 + x2x3 = c/a x1x2 + x1x3 + x2x3 = 9/1 x1x2 + x1x3 + x2x3 = 9 2p² + 2p(8 - 3p) + p(8 - 3p) = 9 2p² - 6p² - 3p² + 16p + 8p - 9 = 0 -7p² + 24p - 9 = 0 (-7p + 3)(p - 3) = 0 -7p+3 = 0 -7p = -3 p = (-3)/(-7) p = 3/7 atau p - 3 = 0 p = 3 x2 = p = 3/7 x1 = 2p = 2(3/7) = 6/7 x3 = 8 - 3p x3 = 8 - 3(3/7) x3 = 8 - 9/7 x3 = 56/5 - 9/7 x3 = 47/7 x1 ⋅ x2 ⋅ x3 = -d/a x1 ⋅ x2 ⋅ x3 = -d/a x1 ⋅ x2 ⋅ x3 = -n/1 x1 ⋅ x2 ⋅ x3 = -n 6/7 ⋅ 3/7 ⋅ 47/7 = -n 846/343 = -n n = -846/343 x2 = p = 3 x1 = 2p = 2(3) = 6 x3 = 8 - 3p x3 = 8 - 3(3) x3 = 8 - 9 x3 = -1 x1 ⋅ x2 ⋅ x3 = -d/a x1 ⋅ x2 ⋅ x3 = -d/a x1 ⋅ x2 ⋅ x3 = -n/1 x1 ⋅ x2 ⋅ x3 = -n 3 ⋅ 6 ⋅ (-1) = -n -18 = -n n = 18 Jadi, nilai n adalah -846/343 atau 18.