i(x)=-0.01x^2+10x+300

解

i (x) = - 0.01 x^{2} + 10 x + 300

x = - 28.89910 \dots - 2.73200 \dots i, x = 1028.89910 \dots - 97.26799 \dots i

解答ステップ

i (x) = - 0.01 x^{2} + 10 x + 300

代用

x = a + bi

i (a + bi) = - 0.01 (a + bi)^{2} + 10 (a + bi) + 300

拡張

- b + ia = (- 0.01 a^{2} + 0.01 b^{2} + 10 a + 300) + i (10 b - 0.02 ab)

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[- b = - 0.01 a^{2} + 0.01 b^{2} + 10 a + 300 a = 10 b - 0.02 ab]

[- b = - 0.01 a^{2} + 0.01 b^{2} + 10 a + 300 a = 10 b - 0.02 ab] : (a = - 28.89910 \dots, a = 1028.89910 \dots, b = - 2.73200 \dots b = - 97.26799 \dots)

代用を戻す

x = a + bi

x = - 28.89910 \dots - 2.73200 \dots i, x = 1028.89910 \dots - 97.26799 \dots i