How do you find all the real and complex roots of $x^3 + 4x^2 + x + 4=0$ ?

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Answer 1 · 2016-02-03T19:51:54

Factor by grouping to find roots:

$x=-4$ , $x=i$ , $x=-i$

Factor by grouping:

$x^3+4x^2+x+4$

$= (x^3+4x^2)+(x+4)$

$= x^2(x+4)+1(x+4)$

$= (x^2+1)(x+4)$

$(x+4)$ is zero when $x=-4$

$(x^2+1)$ is zero when $x=+-i$

So the roots of $x^3+4x^2+x+4 = 0$ are $x=-4$ and $x=+-i$

How do you find all the real and complex roots of x^3 + 4x^2 + x + 4=0x^3 + 4x^2 + x + 4=0?