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 that a) 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 $$ f\left( a_i \right) =b_i,\quad\forall i\in\{ 1,2,\ldots ,n \} . $$b) there exists a polynom $ g\in\mathbb{R} [X] $ of degree at least $ 1 $ which has only real roots and such that $$ g\left( a_i \right) =b_i,\quad\forall i\in\{ 1,2,\ldots ,n \} . $$