ข้อความเดิมเขียนโดยคุณ แฟร์ (ข้อความที่ 167309)

f(x) = a(x^3) + (a^2)(x^2) + x ซึ่งเมื่อหารด้วย x - 1 เหลือเศษ 91
จงหา (b - c)^2

f(1) = a(1) + (a^2)(1) + 1 = 91
a + (a^2) = 90
(a^2) + a - 90 = 0
(a - 9)(a + 10) = 0
a = 9 , -10

f(b) = 0 = f(c) = f(0)

9(x^3) + (81)(x^2) + x = 0
x [ 9(x^2) + 81x + 1 ] = 0
x = 0 , -0.01236 , -8.98764

-10(x^3) + (100)(x^2) + x = 0
x [ -10(x^2) + 100x + 1 ] = 0
x = 0 , -0.00999 , 10.00999
b = -0.00999
c = 10.00999

b - c = -0.00999 - 10.00999 = -10.01998
(b - c)^2 = (-10.01998)^2 = 100.3999992004
ตอบ (b - c)^2 = 100.4