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The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.
In fact, if you use complex number, then a polynomial with degree n has exactly n roots.
So, in particular, a third-degree polynomial can have at most 3 roots.
In fact, in general, if the polynomial has solutions
, then you can factor it as
So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as
But this is a fourth-degree polynomial.
Hey!
Let's write it,
Add
to both sides,
Subtract
from both sides.
Since we don't want a negative variable, we have to divide both sides by
.
Our answer would be,
Thanks!
-TetraFish
Let's write it,
Add
Subtract
Since we don't want a negative variable, we have to divide both sides by
Our answer would be,
Thanks!
-TetraFish