How do you solve this polynomial?
2(x^3)-x^2-1=0
I know how to solve polynomials, but I can't remember how to solve when you can't factor normally.

Question

How do you solve this polynomial?
2(x^3)-x^2-1=0
I know how to solve polynomials, but I can't remember how to solve when you can't factor normally.

blurbendy · Answer

you can simplify this to:

(x-1)(2x^2 + x + 1) = 0

blurbendy · Answer

your solution will depend on if your looking for just the real solutions, or the complex solutions as well

anonymous · Answer

Could you explain to me how you got there? I'm sorry, I just want to learn how to do it too XD

anonymous · Answer

And does that say two x squared DIVIDED by x DIVIDED by 1?

anonymous · Answer

x=1 is a root.
then x=1 is a factor. and then factorise.

blurbendy · Answer

quantity (x - 1) times (2x^2 + x + 1) = 0

blurbendy · Answer

no division

anonymous · Answer

Thanks! But how did you find out that x=1 was a factor?

blurbendy · Answer

(x-1)(2x + x + 1) = 0

consider first (x - 1) = 0

x = 1

blurbendy · Answer

that's your real solution.  you'll get complex solutions if you try to find 2x^2 + x + 1 = 0

anonymous · Answer

Okie dokie. Thanks so much for your help!

blurbendy · Answer

yw.  hope it makes sense