How do I show that 2 + 8x - 2x^3 = 0 has three real solutions?
I know you can say it has at most three solutions from the fundamental theorem of algebra, and I presume the easiest way to show the three solutions are real and not complex is to actually find them... But how ought one to go about this?
I can't see any convenient factoring up the equation..
Moderator edit: This thread has been moved from the Pre-Calculus to the Calculus subforum. This comment is made so that some of the posts (which I choose not to delete) in this thread make sense. For the record, if a question requires differentiation or integration then it is clearly a calculus question and belongs in the Calculus subforum.