Real solutions for a decinary equation
Algebra
Level
3
Find all real x for x^10+2x^9+3x^8+4x^7+5x^6+6x^5+7x^4+8x^3+9x^2+10x+11=0.
1
67
4
-123
0
No real solutions using Newton Raphson
3
2
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1 solution
Clearly, x must be negative. The equation can be written as ( x − 1 ) 2 x 1 2 − 1 2 x + 1 1 , which is positive for all negative x. Thus there are no solutions.