MathDB

Albanian BMO TST 2009 Question 1

Source:

June 4, 2010

functionalgebra unsolvedalgebra

Problem Statement

Given the equation

x^4-x^3-1=0

(a) Find the number of its real roots. (b) We denote by

S

the sum of the real roots and by

P

their product. Prove that

P< - \frac{11}{10}

and

S> \frac {6}{11}