Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
The polynomial \(P(X) = a_0 + a_1X + a_2X^2 + ....+ a_nX^n\) where \(a_0,a_1,...,a_n\) are all real numbers and \(a_0>a_1>a_2>....>a_n>0\). Then which of the following MUST be true:
P(X) always has a real root
P(X) has a complex root z and z ≥1
P(X) has a complex root and z<1
P(X) does not have any complex root
 one year ago
 one year ago
The polynomial \(P(X) = a_0 + a_1X + a_2X^2 + ....+ a_nX^n\) where \(a_0,a_1,...,a_n\) are all real numbers and \(a_0>a_1>a_2>....>a_n>0\). Then which of the following MUST be true: P(X) always has a real root P(X) has a complex root z and z ≥1 P(X) has a complex root and z<1 P(X) does not have any complex root
 one year ago
 one year ago

This Question is Closed

ParthKohliBest ResponseYou've already chosen the best response.1
Always assume a polynomial of this form. Use this for the experiments:\[\rm p(x) = x^2 + 2x + 3\]
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Now see what all is true.
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
@ParthKohli Sorry, didn't get you, can you explain me more?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
In these questions, I always take an example of a polynomial and see what all is true amongst the choices.
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
OK... i am getting it... let me check the choices now.
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
At least it will be complex root if I take your equation of the polynomial. P(X) = \(x^2+2x+3\) x = \(\LARGE\frac{2 \pm \sqrt{412}}{2} = \frac{2 \pm 2\sqrt{2}}{2} = 1 \pm \sqrt{2} i \)
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
So it will be ,,,, 2nd option : P(X) has a complex root z and z ≥1 Right?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Keep taking such equations and you'd get your answer... I think.
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
OK thanks for the shortcut friend...
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
z is the modulus?
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
It is modulus.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
\[\sqrt{(1)^2 + (\sqrt2)^2} = \sqrt{1 + 2} = \sqrt 3\]Yes, you're right
 one year ago

SheldonEinsteinBest ResponseYou've already chosen the best response.1
:) Yeah Yeah Yeah!!! Thanks!
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.