Hubungan Akar-akar Polinomial Derajat 3
Jika polinomial \(ax^3 + bx^2 + cx + d = 0\) memiliki akar-akar \(x_1\), \(x_2\) dan \(x_3\), maka:
\(x_1 + x_2 + x_3 = - \dfrac ba\)
\(x_1 \:.\: x_2 + x_1 \:.\: x_3 + x_2 \:.\: x_3 = \dfrac ca\)
\(x_1 \:.\: x_2 \:.\: x_3 = - \dfrac da\)
Perhatikan tanda (−) selang-seling
b = (−), c = (+), d = (−)
Hubungan Akar-akar Derajat 4
Jika polinomial \(ax^4 + bx^3 + cx^2 + dx + e = 0\) memiliki akar-akar \(x_1\), \(x_2\), \(x_3\) dan \(x_4\), maka:
\(x_1 + x_2 + x_3 + x_4 = - \dfrac ba\)
\(x_1 \:.\: x_2 + x_1 \:.\: x_3 + x_1 \:.\: x_4 + x_2 \:.\: x_3 + x_2 \:.\: x_4 + x_3 \:.\: x_4 = \dfrac ca\)
\(x_1 \:.\: x_2 \:.\: x_3 + x_1 \:.\: x_2 \:.\: x_4 + x_2 \:.\: x_3 \:.\: x_4 = - \dfrac da\)
\(x_1 \:.\: x_2 \:.\: x_3 \:.\: x_4 = \dfrac ea\)
Perhatikan tanda (−) selang-seling
b = (−), c = (+), d = (−), e = (+)