Wow equation

Algebra Level 4

Determine the number of real roots of the equation:x8x7+2x62x5+3x43x3+4x24x+52=0.x^8 - x^7 + 2x^6 - 2x^5 + 3x^4 - 3x^3 + 4x^2 - 4x +\dfrac{5}{2}= 0.

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