Y by GuvercinciHoca, Anshul_singh, Rounak_iitr
Suppose
is a non-constant polynomial with real coefficients, and even degree. Bob writes the polynomial
on a board. At every step, if the polynomial on the board is
, he can replace it with
1.
for a real number
, or
2. the polynomial
.
Can he always find a finite sequence of steps so the final polynomial on the board has exactly
real roots? What about
?
~Sutanay Bhattacharya



1.


2. the polynomial

Can he always find a finite sequence of steps so the final polynomial on the board has exactly


~Sutanay Bhattacharya