How many positive real solutions are there to \(x^{10}+7x^9+14x^8+1729x^7-1379x^6=0\)?
+128460 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
