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45^o rotation gives y=x^3+ax^2+19x+97 (III Soros Olympiad 1996-97 R3 11.2)

Source:

May 31, 2024

geometrygeometric transformationrotation

Problem Statement

It is known that the graph of the function

y = f(x)

after a rotation of

45^o

around a certain point turns into the graph of the function

y = x^3 + ax^2 + 19x + 97

. At what

a

is this possible?