Y by hadikh, Amir Hossein, mostafataheri, Adventure10, Mango247
Consider the second degree polynomial
with real coefficients. We know that the necessary and sufficient condition for this polynomial to have roots in real numbers is that its discriminant,
be greater than or equal to zero. Note that the discriminant is also a polynomial with variables
and
. Prove that the same story is not true for polynomials of degree
: Prove that there does not exist a
variable polynomial
such that:
The fourth degree polynomial
can be written as the product of four
st degree polynomials if and only if
. (All the coefficients are real numbers.)
Proposed by Sahand Seifnashri







The fourth degree polynomial



Proposed by Sahand Seifnashri
This post has been edited 5 times. Last edited by goodar2006, Jun 28, 2012, 5:49 PM