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 realroots iff it has two critical points x1, x2 such that p(x1)p(x2) < 0.

We have to show that, x3 + ax +b =0 has three real roots iff 4a3 +27b2 <0 for any real numbers a…

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.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.2: Remainder And Factor Theorems

Problem 51PS

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Question

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.

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