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2. For a, b e R, show that r3+ ax +b= 0 has three real roots iff 4a3 + 2762 < 0. Remark: This is a Calculus exercise. Explain why f(x) = x³+ ax + b has three real roots iff it has two critical points r1, x2 such that p(x1)p(x2) < 0.

2. For a, b e R, show that r3+ ax +b= 0 has three real roots iff 4a3 + 2762 < 0. Remark: This is a Calculus exercise. Explain why f(x) = x³+ ax + b has three real roots iff it has two critical points r1, x2 such that p(x1)p(x2) < 0.

Advanced Engineering Mathematics
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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This question is from Abstract Algebra. Please answer if you are familiar with the topic and in a clear fashion. Thank you in advance!
2. For a, b e R, show that r+ ax +b= 0 has three real roots iff 4a³ + 276² < 0. Remark: This is a Calculus exercise. Explain why f(x) = x* + ax +b has three real roots iff it has two critical points x1, x2 such that p(x1)p(x2) < 0.
Transcribed Image Text:2. For a, b e R, show that r+ ax +b= 0 has three real roots iff 4a³ + 276² < 0. Remark: This is a Calculus exercise. Explain why f(x) = x* + ax +b has three real roots iff it has two critical points x1, x2 such that p(x1)p(x2) < 0.
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