(b) (i) Given that 1 i is a complex root of the cubic polynomial r- r² + 2, determine the other two roots (without using a calculator). (ii) Hence, (and without using a calculator) determine 5x dr. r³ – x² + 2 (Hint: Use the result of part (a) to write a – x² + 2 = (r – a)(x² + bx + c) for some a, b and c, and use partial fractions.)
(b) (i) Given that 1 i is a complex root of the cubic polynomial r- r² + 2, determine the other two roots (without using a calculator). (ii) Hence, (and without using a calculator) determine 5x dr. r³ – x² + 2 (Hint: Use the result of part (a) to write a – x² + 2 = (r – a)(x² + bx + c) for some a, b and c, and use partial fractions.)
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
Section9.3: Polynomial Equations
Problem 5CQ
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Transcribed Image Text:(b) (i) Given that 1 i is a complex root of the cubic polynomial r- r2 + 2,
determine the other two roots (without using a calculator).
(ii) Hence, (and without using a calculator) determine
5x
dr.
r3 – r² + 2
(Hint: Use the result of part (a) to write
* – x² + 2 = (r – a)(x² + bx + c)
for some a, b and c, and use partial fractions.)
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