Question

POLYNOMIAL SOLUTIONS: (descartes rule of signs)
How many possible positive, negative and complex solutions are there in f(x)= 314x^3+1256x^2-7536 ?

Answer 1

Would -3+/-(i)sqrt3 count as a complex?

Answer 2

well, if it has an 'i' there, yes

Answer 3

would I say 1 positive, and 1 or 0 negative and 2 complex?

Answer 4

Didnt we already do this? XD

Answer 5

Well the sign changes once when x is positive so there is 1 positive solution.

Answer 6

@marissalovescats haha yes but I still am so out of it with putting it all together into words

Answer 7

using Descartes rule of signs, let's see the signs changes
+ 314x^3 + 1256x^2 - 7536
+ -
no yes
so it changed once, from + to -
so 1 real POSITIVE root

now let's check f(-x)

- 314x^3 + 1256x^2 - 7536
yes yes

so, it chanced twice, from - to + and then back to -
so, 2 OR 0 real NEGATIVE roots

Answer 8

So it should be 1 positive 2 imaginary. But i could be wrong.

Answer 9

When we solves it earlier there were imaginary sooo i think im right.

Answer 10

so is a 3rd degree equation, so there'll be 3 roots

so, is only 1 real positive, and 2 real negative, that leaves room for no complex
OR
1 real positive, and 0 real negative, so enough room for 2 complex ones

Answer 11

1 real positive and 0 real negative and 2 complex I think that makes sense !