(i) Consider the polynomial f(x)= x³8x² + x +52. Please accept as a given that the polynomial f(x) has three real roots in [-10, 10]. (a) Let then 71, 72, 73 be the roots of f(x) written in increasing order. For each of the roots ri, find a pair of integer numbers m, m + 1 that bracket the root r;: 1) r₁ is between 2) 72 is between and Yes No and 3) r3 is between (b) Now, according to (a), is it true that the polynomial f(x) has a unique root in the closed interval [-3, -2]? and
(i) Consider the polynomial f(x)= x³8x² + x +52. Please accept as a given that the polynomial f(x) has three real roots in [-10, 10]. (a) Let then 71, 72, 73 be the roots of f(x) written in increasing order. For each of the roots ri, find a pair of integer numbers m, m + 1 that bracket the root r;: 1) r₁ is between 2) 72 is between and Yes No and 3) r3 is between (b) Now, according to (a), is it true that the polynomial f(x) has a unique root in the closed interval [-3, -2]? and
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(Bisection Method). All numerical answers should be rounded to 6-digit floating-point
numbers.
(i) Consider the polynomial
f(x) = x³ - 8x² + x +52.
Please accept as a given that the polynomial f(x) has three real roots in [-10, 10].
(a) Let then 71, 72, 73 be the roots of f(x) written in increasing order. For each of the
roots ri, find a pair of integer numbers m, m + 1 that bracket the root r;:
1) 7₁ is between
2) r2 is between
and
and
3) 13 is between
(b) Now, according to (a), is it true that the polynomial f(x) has a unique root in the
closed interval [-3, -2]?
Yes
No
and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61822fce-02ce-40dd-9c1c-3513c1e5aa8b%2Fa3381ac7-553d-49a6-828a-220e10ea1958%2Fwvjfvj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(Bisection Method). All numerical answers should be rounded to 6-digit floating-point
numbers.
(i) Consider the polynomial
f(x) = x³ - 8x² + x +52.
Please accept as a given that the polynomial f(x) has three real roots in [-10, 10].
(a) Let then 71, 72, 73 be the roots of f(x) written in increasing order. For each of the
roots ri, find a pair of integer numbers m, m + 1 that bracket the root r;:
1) 7₁ is between
2) r2 is between
and
and
3) 13 is between
(b) Now, according to (a), is it true that the polynomial f(x) has a unique root in the
closed interval [-3, -2]?
Yes
No
and
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