MathDB

Each of two different lines parallel to the the axis

Ox

have exactly two common points on the graph of the function

f(x)=x^3+ax^2+bx+c

. Let

\ell_1

and

\ell_2

be two lines parallel to

Ox

axis which meet the graph of

f

in points

K_1, K_2

and

K_3, K_4

, respectively. Prove that the quadrilateral formed by

K_1, K_2, K_3

and

K_4

is a rhombus if and only if its area is equal to

6

units.

Problem Statement