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Question

Solve: x4x3+x2x+1=0

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Solution

f(x)=x4x3+x2x+1
f(0)=1
f(x)=4x33x2+2x1
f′′(x)=12x26x+2=2(6x23x+1)
We can see that the second derivative doesn't go to zero for any x.
Thus, first derivative is an monotonically increasing function.
First derivative is zero at 0.6<x<0.7
The function gives f(0.6)>0 and f(0.7)>0
So, f(x)0 for all x

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