Question

explain how each theorem can be used in determining the solutions for f(x)=x^3+4x^2-x-10

fundemental theorem of algebra and descartes rule of signs and rational root theorem

Answer 1

@jim_thompson5910

Answer 2

how far did you get?

Answer 3

i got no where

Answer 4

ive tried learning the theorems and can't

Answer 5

What's the degree of this polynomial?

Answer 6

5?

Answer 7

the highest degree is 3 but combined all together i think it is 6

Answer 8

The largest exponent is 3, so that's the degree

Answer 9

is this for the first theorem?

Answer 10

That means there are at most 3 real roots. There could be less than 3 real roots (say 1 real root and 2 complex roots). This is based off the fundamental theorem of algebra which says "an nth degree polynomial has at most n real roots"

Answer 11

but i dont get how that would determine a solution for the problem though thats where im lost at

Answer 12

well how many real solutions can we have? What's the max number?

Answer 13

3 is the most number of real solution's we can have

Answer 14

so that's handy info to know when solving a polynomial and finding the roots

Answer 15

it tells you when you have found all of the solutions and you don't need to look anymore once you've done so

Answer 16

how does descartes rule of signs help?

Answer 17

im not familiar with these rules thats why

Answer 18

have a look at this page

http://www.purplemath.com/modules/drofsign.htm

and tell me if that helps or not