Consider the polynomial: f = 2X¹ +aX³ +3X²+bx+c € R[X] with roots X₁, X2, X3, X4 € C. a) Calculate: Σ (xi - xj)² 1
Consider the polynomial: f = 2X¹ +aX³ +3X²+bx+c € R[X] with roots X₁, X2, X3, X4 € C. a) Calculate: Σ (xi - xj)² 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Consider the polynomial:
f=2X^4+aX^3+3X^2+bX+c belong to R[X],
with roots x_1, x_2, X_3, X_4 belong to C.
Please check the attached picture for details.
I need complete solution with explanation please.
All three subpoints are subpoints for the same problem and they are conected between them, but if it is not possible to solve them all please solve what you can, thank you in advance.
![Consider the polynomial:
f = 2x4 + aX3+ 3X? + bX + c € R[X]
with roots x1, X2, X3, X4 E C.
a) Calculate:
|
1<i<j<4
and then prove that for | a | <4 the polynomial has at
most two real roots.
b) For | a| = 4 determine b and c so that f has all roots
real.
c) For | a |> 4 prove that there is b and c in R such that
f has all roots real.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde54a8a1-129b-452f-b5d1-f7f157f4c8c4%2F94a4fb98-ca13-4390-981a-49820e6e3ecd%2Fipvoq3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the polynomial:
f = 2x4 + aX3+ 3X? + bX + c € R[X]
with roots x1, X2, X3, X4 E C.
a) Calculate:
|
1<i<j<4
and then prove that for | a | <4 the polynomial has at
most two real roots.
b) For | a| = 4 determine b and c so that f has all roots
real.
c) For | a |> 4 prove that there is b and c in R such that
f has all roots real.
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