g(x) = (x - 5)^2 + 2x^3
At the root this function is equal to 0
(x - 5)^2 + 2x^3= 0
Rearrange:
(x - 5)^2 = -2x^3
Now if you plot these two functions you need to check how many times they intersect. For this you do not need to be precise just scetch approximately.
If you do that, you will see that they meet once. I cannot really use this site to plot, but you can use other tools for that if you do not know how to do it.
