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.
Answer:
Exact form : <u>10√11</u>
Step-by-step explanation:
Answer:
Great work!
Step-by-step explanation:
These kind of questions are calculated through Riemann Sum. You can evaluate any definite integral using the Riemann Sum. It should be in the following form:
f(x)dx on the interval [a, b], or
Now f(x) is simply y. Therefore in this example y = x^3 - 6x. We just need the sufficient amount of data to apply the Riemann Sum, including the interval [a, b] that bounds the area, and the the number of rectangles 'n' that we need to use.
Consider an easier approach to this question: (First attachment)
Graph: (Second Attachment)
For this case what we can do is the following rule of three:
2/3 of a box ------> 1/2 minutes
x of a box ---------> 1 minute
Clearing x we have:
x = (1 / (1/2)) * (2/3)
Rewriting:
x = 2 * (2/3)
x = 4/3
Answer:
the number of boxes per minute that the machine packs is:
x = 4/3
