1. ## Roots related question

Hey guys I was having trouble with this question can someone plesase explain it to me in detail. thanks much appreciated.

2. Originally Posted by ballaholic8
Hey guys I was having trouble with this question can someone plesase explain it to me in detail. thanks much appreciated.
$x^3 - 3^3 = (x - 3)(x^2 + 3x + 9)$.

Therefore the roots of $x^3 - 27$ are x = 3 and the solutions to $x^2 + 3x + 9 = 0$.

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A polynomial with roots $x = 3 \pm i$ and $x = -4$ is

$a (x - [-4])(x - [3 + i])(x - [3 - i]) = a (x + 4)([x - 3] - i)([x - 3] + i)$ $= a (x + 4)([x - 3]^2 + 1) = a(x + 4)(x^2 - 6x + 10)$

where a is any real number except zero.