- #1

- 349

- 0

## Main Question or Discussion Point

Here is another problem which is driving me insane!I just need a hint on how to proceed!

To Solve:-

p^7 + p^3 - p^2 + 1 =0

here p = dy/dx

To Solve:-

p^7 + p^3 - p^2 + 1 =0

here p = dy/dx

- Thread starter heman
- Start date

- #1

- 349

- 0

Here is another problem which is driving me insane!I just need a hint on how to proceed!

To Solve:-

p^7 + p^3 - p^2 + 1 =0

here p = dy/dx

To Solve:-

p^7 + p^3 - p^2 + 1 =0

here p = dy/dx

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 955

My suggestion- go insane!

- #3

- 349

- 0

I asked my tutor and he said that there will be atleast 1 real root

=> p=k

or y=kx + c

From here i am thinking ahead!

- #4

saltydog

Science Advisor

Homework Helper

- 1,582

- 3

So we look for solutions of the form y=mx+b, plug it in, get a polynomial in m and solve for the roots. So there's one real root. So we find it numerically (I ain't proud), and then we get the solution:

[tex]y(x)=m_rx+b[/tex]

So, how do we know if there are other solutions?

- #5

- 349

- 0

The same thing i asked him!saltydog said:So, how do we know if there are other solutions?

He said our aim is to get just 1 family of curves of solution!

The other six can be complex,real who knows!

- #6

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 955

(Yes, the polynomial p^7 + p^3 - p^2 + 1 =0, by DesCartes' "rule of signs", has one

- #7

- 349

- 0

Your Predictions!!

(1) 1 negative real root and 3 pair of conjugate complex roots

I understand that it can have 3 pair of conjugate complex roots-but how do you say that real root will be negative?

(2) 1 negative real root, 2 positive real roots, and 2 pair of conjugate comples roots

How are you able to tell the signs??

I have taken the Complex Analysis Course last semester but i haven't come across any such theorem which tells about the sign!

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 722

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 3K

- Last Post

- Replies
- 4

- Views
- 6K

- Last Post

- Replies
- 7

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 0

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 6K