z^4+z^3+z^2+z+1=0

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to multiply both sides by `z - 1`  such that:

`(z-1)(z^4+z^3+z^2+z+1) = 0*(z-1)`

You need to convert the product to the left side into a difference of powers such that:

`z^5 - 1 = 0 => z^5 = 1 => z^5 = root(5)1 => z = 1`

Since the graph below representing the function `f(x)=x^4+x^3+x^2+x+1` , does not intercept x axis, hence, the equation has no real roots but 4 complex roots.

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