Using graphs to understand a question.

Algebra Level 3

Graph of f(x) = x^5 - 2x^3 + x

The curve $$f(x) = x^5 - 2x^3 + x$$ has a local minimum at $$(-0.447, -0.286)$$. How many real solutions are there to the equation $$x^5 - 5x^4 + 8x^3 - 4x^2 + 1 = 0$$ ?

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