9

Part of 2022 MMATHS

Problems(2)

2022 MMATHS Team Online p9 - sum of roots of monic cubic polynomial =1

Source:

f

be a monic cubic polynomial such that the sum of the coefficients of

f

5

and such that the sum of the roots of

f

1

. Find the absolute value of the sum of the cubes of the roots of

f

algebrapolynomialsum of rootsMMATHS

2022 MMATHS Individual p9 - 2 sequences

Source:

Suppose sequence

\{a_i\} = a_1, a_2, a_3, ....

a_{n+1} = \frac{1}{a_n+1}

for all positive integers

n

b_k

for positive integers

k \ge 2

to be the minimum real number such that the product

a_1 \cdot a_2 \cdot ...\cdot a_k

does not exceed

b_k

for any positive integer choice of

a_1

\frac{1}{b_2}+\frac{1}{b_3}+\frac{1}{b_4}+...+\frac{1}{b_{10}}.