The parts where I was to prove the postive or negative roots made a lot of sense thank you, but can you re-explain showing that if z is any root of p(x), then |z| < 170
Hello everyone!
I have this polynomial: $p(x) =$ $$1 + \sum_{k=1}^{13}\frac{(-1)^k}{k^2}x^k$$
- I'm supposed to show that this polynomial must have at least one positive real root.
- I'm supposed to show that this polynomial has no negative real roots.
- And I'm supposed to show that if $z$...
Oh, okay I think I'm on the right path. I have grouped the terms and I have something that looks like this:
-14k2 + 4k + 1 + 2ik2 + 3ik = 0
This is the closest I can get to that experession. Also, what do you mean by what must be true of $a$ and $b$?
I'm not too sure I understand what you mean MarkFL. :confused:
I have substituted (k + 1)/k into each "x" in the polynomial. The only path forward I see is to expand and simplify.
Okay, so only two questions per thread.
My last question is as follows:
Find all values of k (which may be complex numbers) such that kx - (k + 1) is a factor of the polynomial x2 + (2 + 3i)x - (17 + i)
Thanks for the help :)
I've been trying to do the calculations myself but how did you get 16 + 24i?
The question I am asking is referring to line 7.
Nevermind, I figured it out :p
Hello everyone, I'm new to this forum. I have this Linear Algebra question that I have no clue how to solve. Any help would be much appreciated. :)
The question goes as follows:
The polynomial p(x) = x3 + kx + (3 - 2i)
where k is an unknown complex number. It is given to you that if p(x) is...