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.


`(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=\frac{1\pm√(1-12)}2=\frac12\pm i\frac{√(11)}2`