Steven G
Elite Member
- Joined
- Dec 30, 2014
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For a polynomial I know that complex and irrrational roots occur in pairs.
In the equation x3-x-2=0 the only possible rational roots are +/- 2. In fact neither of them are roots.
If there are 2 complex roots, then when you multiply them you get a quadratic. You can only multiply that by a linear factor to get the cubic. Now linear factor yield a single root. In this case should we not have 2 complex roots and a rational root??
If two roots were irrational (and they do come in pairs) then the 3rd root must be rational!
What am I missing here?
In the equation x3-x-2=0 the only possible rational roots are +/- 2. In fact neither of them are roots.
If there are 2 complex roots, then when you multiply them you get a quadratic. You can only multiply that by a linear factor to get the cubic. Now linear factor yield a single root. In this case should we not have 2 complex roots and a rational root??
If two roots were irrational (and they do come in pairs) then the 3rd root must be rational!
What am I missing here?
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