多項式(9)
Author: 藍邦偉  老師

設f(x)=a(x+1)(x-2)(x-4),a<0

=a(x³-5x²+2x+8)

=ax³-5ax²+2ax+8a

$ ⇒b=-5a>0,c=2a<0,d=8a<0 $

⇒f(x)<0⇒-1<x<2或x>4

 f(-2)=-8a+4b-2c+d

-f(-2)=15a<0

=a(-1)×(-3)×(-5)=-15a>0

x

y

y=f(x)

n = 0 (slider from 0 to 9, step 1)
A = (-1, 0)
B = (2, 0)
C = (4, 0)
D = (-1.16, 0.84)
f = Polynomial({A, B, C, D})
poly1, a, b, c, d = Polygon(Corner[1], Corner[2], Corner[3], Corner[4])
E: (x(Corner[1]), 0)
F: (x(Corner[3]), 0)
u = Vector(E, F)
G: (0, y(Corner[1]))
H: (0, y(Corner[3]))
v = Vector(G, H)