多項式(8)
Author: 藍邦偉　老師

E(m,n)

f(x)=a(x+4)(x+1)(x-3)²,a<0

⇒f(0)=a×4×1×9=-2⇒a=-\frac{1}{18}

⇒f(x)=-\frac{1}{18}(x+4)(x+1)(x-3)²=0

⇒x=-4,-1,3,3,f(x)=0沒有虛根

$f(x)≥0⇒-4≤x≤-1或x=3 $

$ 如圖,y=x與y=f(x)交於兩點 $

$ ⇒f(x)=(x-m)Q(x)+n⇒f(m)=n $

如圖,∀x∈\mathbb{R}⇒f(x)≤n

x

y

y=f(x)

n = 0 (slider from 0 to 8, step 1)
A = (-4, 0)
B = (-1, 0)
C = (3, 0)
D = (0, -2)
F = (-2.02, 2.82)
f = Polynomial({A, B, C, D, F})
poly1, a, b, c, d = Polygon(Corner[1], Corner[2], Corner[3], Corner[4])
E = Point(f)
I: (x(Corner[1]), 0)
H: (x(Corner[3]), 0)
u = Vector(I, H)
G: (0, y(Corner[1]))
J: (0, y(Corner[3]))
v = Vector(G, J)