RO-NMO 2017 Problem 122

Let be a natural number $n$ and $2n$ real numbers $b_1,b_2,\ldots ,b_n,a_1<a_2<\cdots <a_n.$ Show thata) if $b_1,b_2,\ldots ,b_n>0,$ then there exists a polynomial $f\in\mathbb{R}[X]$ irreducible in $\mathbb{R}[X]$ such that $$f\left( a_i \right) =b_i, \forall i\in\{ 1,2,\ldots ,n \} .$$ b) there exists a polynom $g\in\mathbb{R} [X]$ of degree at least $1$ which has only real roots and such that $$g\left( a_i \right) =b_i, \forall i\in\{ 1,2,\ldots ,n \} .$$