Octopus Poly

Algebra Level 5

Let

$$\displaystyle f(x) = 5x^{88} + ax^{5} + bx^{2} - cx -10$$

Given

$$a, b, c \in \mathbb R$$

$$f(2) = 5, f(4) = -5$$

Then find the minimum number of real roots of $$f(x)$$

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