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How many positive real solutions are there to \(x^{10}+7x^9+14x^8+1729x^7-1379x^6=0\)?

 May 10, 2019
 #1
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x^10 + 7x^9 + 14x^8 + 1729x^7 - 1379x^6  = 0

 

x^6 ( x^4 + 7x^3 + 14x^2 + 1729x - 1379)  = 0        [ we know that x = 0 is a solution ]

 

x^4 + 7x^3  + 14x^2 + 1729x - 1379  = 0

 

Using the Rational Zeroes Theorem...the possible factors of 1379   are    ± [1, 7, 197, 1379]

 

However.....none of these are roots

 

The graph here shows that there is only one positive real solution :

 

https://www.desmos.com/calculator/u9lxz5cq5q

 

 

cool cool cool

 May 10, 2019

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