6. Let ao, a1, a2, a3, a4 be constant real numbers such that a1 a2 a3 + + + + a4 = 0. 5 4 3 2 Show that the polynomial P(x) = ax² + a₁x³ + a₂x² +a3x+a4 has at least one zero between 0 and 1. (Hint: Consider a1 4 a2 5 a3 f(x) = 2x³ + 2/1x²¹ +23²x³² +22³x² + Show that Rolle's theorem applies to f(x) on the interval [0, 1]. Deduce that P(x) has a 0 in [0, 1]).
6. Let ao, a1, a2, a3, a4 be constant real numbers such that a1 a2 a3 + + + + a4 = 0. 5 4 3 2 Show that the polynomial P(x) = ax² + a₁x³ + a₂x² +a3x+a4 has at least one zero between 0 and 1. (Hint: Consider a1 4 a2 5 a3 f(x) = 2x³ + 2/1x²¹ +23²x³² +22³x² + Show that Rolle's theorem applies to f(x) on the interval [0, 1]. Deduce that P(x) has a 0 in [0, 1]).
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
![6. Let ao, a1, a2, a3, a4 be constant real numbers such that
a1 a2 a3
+ + + + a4 = 0.
5 4 3 2
Show that the polynomial P(x) = ax² + a₁x³ + a₂x² +a3x+a4 has at least one zero between
0 and 1. (Hint: Consider
a1 4
a2
5
a3
f(x) = 2x³ + 2/1x²¹ +23²x³² +22³x² +
Show that Rolle's theorem applies to f(x) on the interval [0, 1]. Deduce that P(x) has a 0 in
[0, 1]).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f647d9f-6880-40dd-a686-e7d1674263c8%2F8ff9aa68-ed99-464a-9bb8-8296626bd78a%2F2vrhdxl_processed.png&w=3840&q=75)
Transcribed Image Text:6. Let ao, a1, a2, a3, a4 be constant real numbers such that
a1 a2 a3
+ + + + a4 = 0.
5 4 3 2
Show that the polynomial P(x) = ax² + a₁x³ + a₂x² +a3x+a4 has at least one zero between
0 and 1. (Hint: Consider
a1 4
a2
5
a3
f(x) = 2x³ + 2/1x²¹ +23²x³² +22³x² +
Show that Rolle's theorem applies to f(x) on the interval [0, 1]. Deduce that P(x) has a 0 in
[0, 1]).
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