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# Strange functions

Let $$f_r(x)= x(x-1)(x-2)(x-3) + r$$, where $$r$$ is a real number. Then:

• Does $$f_r(x)$$ have a real root for every value of $$r$$?

• Does $$f_r(x)$$ have a repeated root for finitely many values of $$r$$?

Note by Paramjit Singh
2 years, 8 months ago