2. For each of the following polynomials find its factor and its roots.а. (х3 — Зх2 + 5х — 6)b. (х3 + 3x2 — 9х + 5)с. (бх3 — х2 — 2х)-- B. Remainder Theorem and Factor Theorem (Week 2)

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Answered: 2. For each of the following…

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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Multiply: а. (х + 8)(х — 8) b. (9х + 5у)(9х — 5у) (ба?ь — зь) (ба'ь + 3b). С.
Find the following. If the operation is not possible, state this.
What expression gives the values of the roots (if any) of the quadratic equation ах + bx + с %3D0 ас X1,2 2a b± vb? - 4ac X1,2 2a ас X1,2 2а -6+ vb? 4ас X1,2 = 2a
M- М3: АСТ2 Activity Name: Polynomial Evaluations Instructions: Evaluate the following polynomials. Show your solutions. • By Substitution Method (6) 1. 2. 3. 4. By Horner's Method (9) 1. 2. 3. 4. Given: 1. P(x) = 2x4 - 3x3 + x2 - 2x + 3 X = 2 2. P(x) = 2x5 + 7x - 6x + 5 X = 4 3. P(x) = -3x + 8x+ - 6x3 -2x -6 X = -3 4.P(x) = 8x4 + 7x3 - 5x2 -4x + 5 x = 1/3
Advanced Math Question
If ø (a) and øb) are of opposite signs and the real root of the equation ø (x) = 0 is found by false position method, the first approximation x1, of the root is ... ab +(a) Þ(½) $(a)-o(b) A a (b)-b ¢(a} +(b)-$(a) B a ¢(b)+b ¢La) (b)++(a) a o'(b)+b ¢'f«) $(b)+ ¢(a) D
If a, ß be the roots of ax² + 2bx + c = 0 and a +8, B+ 8 be those of Ax² + 2Bx+C =0, then 6² 2 ac the value of is - AC A² (a) q² (c) 0 A 2 B² - - (b) (d) 1
2. Find the sum of the coefficients of the polynomial obtained by fully expanding (x - 2). С. 1 А. -2 В. -1 D. 2 E. 4
Answer the following. Show the solution and final answer.
b) The polynomial, fW) =2x" +mz -3, where m and n are real constants, is divisible by (x+1) but leaves a femiAder remainder of 156 when divided by (X-3). Find the valves of n and m.
For what values of the parameters a, b and c is the polynomial f(x) divisible by the polynomial g(x).f(x)= х3 + ах + вg(x)= х2 + сх +1

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2. For each of the following polynomials find its factor and its roots. (х3 — Зх2 + 5х — 6) b. (x3 + 3x2 — 9х + 5) с. (6х3 — х2 — 2х) а. -