Question

According to the FTA theorem, this equation has how many solutions? x^3 + 4x^2 – 75 = 0

Answer 1

whats the degree of equation ?

Answer 2

What do you mean by degree?

Answer 3

degree or order, they mean the same

Answer 4

they mean, highest exponent

Answer 5

3

Answer 6

correct :D

Answer 7

So that's the answer?

Answer 8

Wow...that's more simple than I expected.

Answer 9

FTA says, if an equation has a degree of 3, then it will have exactly 3 solutions

Answer 10

if an equation has a degree of 100, then it wll have exactly 100 solutions

Answer 11

more generally, we say :
if an equation has a degree of \(\textbf{n}\), then it will have exactly \(\textbf{n}\) solutions.

Answer 12

Could you help me find the three solutions?

Answer 13

i dont think so, it looks complicated to work analytically using Rational Roots & Descartes rule of signs.

Answer 14

oh :(

Answer 15

this particular equation, as i dont see any rational roots that satisfy this equation

Answer 16

Can you tell me what type of function this is?

Answer 17

we can call it a cubic function

Answer 18

since it has a degree of 3

Answer 19

Could I graph it without finding the solutions?

Answer 20

do u have geogebra ?

Answer 21

I could get it? Could I find the solutions with the program?

Answer 22

here you may see the graph :

http://www.wolframalpha.com/input/?i=x%5E3+%2B+4x%5E2+%E2%80%93+75+%3D+0

Answer 23

but ur teacher wont give u marks if u dont show the work

Answer 24

clearly it doesnt have any rational solutions,

Answer 25

I know. I just don't know how to do it. I'm homeschooled...so it's difficult to understand the work.

Answer 26

it has 1 real solution , and 2 complex solutions

Answer 27

i get u, this particular equation is very tough, ask ur teacher only in DBA how to go about solving this problem :)

Answer 28

Okay, thank you..

Answer 29

good luck !