Question

Can someone solve this problem? Please? I have been stuck on it for awhile now. X^3+2x+3=0

Answer 1

Notice that when $x=-1$, you have

$(-1)^3+2(-1)+3=-1-2+3=0$

so $x=-1$ is a solution, and the cubic has $x+1$ as a factor. This means you can divide to get another quadratic factor and thus two more solutions.

$\dfrac{x^3+2x+3}{x+1}=x^2-x+3$

So,

$x^3+2x+3=(x+1)(x^2-x+3)=0$

You can use the quadratic formula here:

$x=\dfrac{1\pm\sqrt{1-12}}2=\dfrac12\pm i\dfrac{\sqrt{11}}2$