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TIFR Mathematics 2022 | Part B | Question-12

Answer whether the following statements are True or False.

Let $f_{1}, f_{2}, f_{3}, f_{4} \in \mathbb{R}[x]$ be monic polynomials each of degree exactly two. Then there exist a real polynomial $p \in \mathbb{R}[x]$ and a subset $\{i, j\} \subset\{1,2,3,4\}$ with $i \neq j$, such that $f_{i} \circ p=c f_{j}$ for some $c \in \mathbb{R}$.

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