@jim_thompson5910 . Ah, I hate to bug you with this, but I love the way that you explain this, it is very helpful.

How many solutions does this equation have? x^7-2x^6+3x^2=17 - I do understand that this would turn to x^7-2x^6+3x^2-17=0

Question

@jim_thompson5910 . Ah, I hate to bug you with this, but I love the way that you explain this, it is very helpful. 

How many solutions does this equation have? x^7-2x^6+3x^2=17   - I do understand that this would turn to x^7-2x^6+3x^2-17=0

anonymous · Answer

Oh, I do understand that the answer is seven, but I would like to understand HOW to figure it out. ><

jim_thompson5910 · Answer

well unfortunately we can't find all of the solutions exactly due to the very complicated nature of the polynomial however, we can use the fundamental theorem of algebra http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

anonymous · Answer

$$\huge x^\color{red}7-2x^6+3x^2-17=0$$

jim_thompson5910 · Answer

that basically says: a polynomial of degree n has n complex solutions

so for instance, a cubic like this one: y = x^3 - 7

has 3 complex solutions because the degree is 3 (degree = largest exponent)

jim_thompson5910 · Answer

satellite73 went ahead and highlighted the largest exponent (aka degree) of your given polynomial

anonymous · Answer

Okay, I am trying to understand what you mean, I could be over thinking it... but I'm not sure...

anonymous · Answer

You probably have to factor this to see how many real roots it has.

anonymous · Answer

or just graph it.

jim_thompson5910 · Answer

Euphoricarts what do you have in mind so far?