11.7

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(2)

integer P(x) = n has m roots (V Soros Olympiad 1998-99 Round 1 11.7)

Source:

For what is the smallest natural number

n

there is a polynomial

P(x)

with integer coefficients, having

m

different integer roots, and at the same time the equation

P(x) = n

has at least one integer solution if: a)

m = 5

m = 6

algebrapolynomial

sinx + arcsinx > 2x (V Soros Olympiad 1998-99 Round 3 11.7)

Source:

Prove that for all positive and admissible values of

x

the following inequality holds:

\sin x + arc \sin x>2x

inequalitiesalgebratrigonometry