1. Find the quotient of x3 −5x2 −2x+ 24 by x−4, and then divide the quotient by x−3. What are the roots of x3−5x2−2x + 24=0? 2. Given that x4 −2x3 −7x2 +8x+12 = 0 has the roots −1 and 2, find the quadratic equation whose roots are the remaining two roots of the given equation, and find these roots.

x-4x2-x-6x3-5x2-2x+24-x3∓4x2-x2-2x+24∓x2±4x-6x+24-6x+2400 ∴x3-5x-2x+24=x2-x-6 x-4 —∗…

Answered: 1. Find the quotient of x3 −5x2 −2x+ 24…

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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1. Find the quotient of x³ −5x² −2x+ 24 by x−4, and then divide the quotient by x−3. What are the roots of x³−5x²−2x + 24=0?

2. Given that x⁴ −2x³ −7x² +8x+12 = 0 has the roots −1 and 2, find the quadratic equation whose roots are the remaining two roots of the given equation, and find these roots.

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