多項式(12)
Author: 藍邦偉　老師

C(3,0)

A(1,6)

$ ∵x=1為對稱軸∴B(-1,0) $

$ 又\Delta ABC與\Delta ABD面積相等 $

$ ∴\overline{BC}=\overline{BD}⇒D(-5,0)

$ 設g(x)=a(x-3)(x+1)(x+5) $

$ g(1)=6=a×(-2)×2×6⇒a=-\frac{1}{4} $

$ ∴g(x)=-\frac{1}{4} (x-3)(x+1)(x+5)$

$ 設f(x)=b(x-3)(x+1) $

$ f(1)=6=b×(-2)×2 $

⇒b=-\frac{3}{2}

$∴ f(x)=-\frac{3}{2}(x-3)(x+1) $

$ ∴f(0)-g(0)=\frac{9}{2}-\frac{15}{4}=\frac{3}{4} $

A_1 = (-5, 0)
B = (-1, 0)
C = (3, 0)
A = (1, 6)
f = Polynomial({C, B, A})
E = Point(yAxis)
v = Vector(E, E + (0, 9.5))
D = Mirror(C, B)
u = Vector(A_1 - (1, 0), C + (1.7, 0))
n = 0 (slider from 0 to 12, step 1)
F = (-13.581911506295066, 7.721288361717558)
F_1: F + (3.5, 0)
F_3: F + (0, 1.7)
F_2: F_1 + F_3 - F
g = Polynomial({A, B, C, D})
G = Intersect(f, x = 0)
H = Intersect(g, x = 0)