Wow equation

Algebra Level 4

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

2 5 6 8 4 0 1

Rohit Udaiwal by Rohit Udaiwal , 20, India

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1 solution

Rishabh Jain
Dec 26, 2015

10 Helpful 0 Interesting 0 Brilliant 0 Confused

Awesome solution

Anirban Mandal - 5 years, 5 months ago

Nice solution.

Another way is to draw its graph.

Dev Sharma - 5 years, 5 months ago

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Can we use Descartes rule of signs here ? @Dev Sharma

A Former Brilliant Member - 5 years, 5 months ago

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it only gives max no of real roots, not exact. I guess.

Dev Sharma - 5 years, 5 months ago

In simple words max value of |2(x)(x-1)| is 1/2 while that of x^6....is less than 10( as x≠1). Therefore product cannot equal -5.

Rishabh Jain - 5 years, 5 months ago

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