MathDB

(a) Find the value of the real number

k

, for which the polynomial

P(x)=x^3-kx+2

has the number

2

as a root. In addition, for the value of

k

you will find, write this polynomial as the product of two polynomials with integer coefficients. (b) If the positive real numbers

a,b

satisfy the equation

2a+b+\frac{4}{ab}=10,

find the maximum possible value of

a

Problem Statement