nilai p dan q adalah:

p³ - 3pq - p² + 4p > 0

misal p = 1, q = 1

Pembahasan :

f(x) = x³ + p(x²-3) - qx

g(x) = x³ + (p-2)²-q(x+3)

-----------------------------------(-)

px²-3p-(p-2)²+3q

= px²+(3q-3p-p²+4p-4) = 0

a = p

b = 0

c = (3q-3p-p²+4p-4)

punya 2 faktor:

D > 0

b²-4ac > 0

0 - 4p(3q-3p-p²+4p-4) > 0

-12pq+12p²+4p³-16p²+16p > 0

-3pq +3p² + p³ - 4p² + 4p > 0

p³ - 3pq - p² + 4p > 0

misal p = 1

1³ - 3 1.q - 1² + 4 .1 > 0

1 - 3q -1 + 4 > 0

4 > 3q

q < 4/3

misal q = 1

f(x) = x³ + p(x²-3) - qx

g(x) = x³ + (p-2)²-q(x+3)

f(x) = x³ + 1.(x²-3) - 1.x

= x³+ x² - x -3

g(x) = x³ + (1-2)²-1.(x+3)

= x³ - x - 2

jika p = 1 dan q = 1

setelah dicek ternyata benar f(x) dan g(x) berpotongan di dua titik.