If P(x) is a polynomial of odd degree, show that the equation p(x)=0 has at least one solution.

Question

dallascowboys88 · Answer

It Doesnt because its x=0 and 0 doesnt have a soulution because its nothing but just a plain old 0.and it has no function either.:)

dallascowboys88 · Answer

0 is like not even a numbe or whatever u wanna call it.but its like its just there for the heck of it.

dallascowboys88 · Answer

and because no number will ever be less than 0 unless your using a negative number.

aabomosalam1998 · Answer

Your answer is not clear to me, I cannot translate my thoughts into a mathematical solution. If the polynomial is defined and continuous on some closed interval [a,b] and f(a) and f(b) have opposite signs then f(c)=0 for at least one point c in (a,b). 
Odd integers: 1, 3, 5, 7...
2n-1 is the formula describing this arithmetic sequence.

aabomosalam1998 · Answer

@zepdrix

zepdrix · Answer

Remember what makes an odd function special?
It satisfies this property: $\large\rm f(-x)=-f(x)$

zepdrix · Answer

Woops, I mean intermediate value theorem.
That's the one, right?

will.h · Answer

Zep I think it has nothing to do with that. It's about odd degree polynomial like this
F(x) = x^3 + x^2 + x

zepdrix · Answer

Oh oh odd `degree`, woopssss :((

will.h · Answer

According to the fundamental theorem of algebra we will have At least 3 solutions for an odd degree polynomial like the example I listed

aabomosalam1998 · Answer

For large values of x will the function approximately equal to the first term of the polynomial and how can I show mathematically  that the function is sometimes positive and sometimes negative in general not for a specific odd degree polynomial.

will.h · Answer

Okay so there are 2 things that effect the nature of the solutions of a polynomial 
Consider the following polynomial
x^3 + x^2 + 9
Now 1st you will need to find the factors of 9 and then the factors of (1) the leading coefficient

Q 9: +-1,  +-3,  +-9
P 1: +-1
And then you will have to divide 
Q/P factors to define the possible solutions 
(so in general those Q and P) are what can determine the nature of the solutions whether complex of positive or negative solutions.