MathDB

The game involves two players

A

and

B

. Player

A

sets the value of one of the coefficients

a, b

c

of the polynomial

x^3 + ax^2 + bx + c.

Player

B

indicates the value of any of the two remaining coefficients . Player

A

then sets the value of the last coefficients. Is there a strategy for player A such that no matter how player

B

plays, the equation

x^3 + ax^2 + bx + c = 0

to have three different (real) solutions?

Problem Statement