Solve Q20, 21 & 22 showing clearly all steps involved 14. If x + 1 is a common factor of x³ – 3x + a and x* – 3x’– ax +b thenA. 2a = b B. b = 0C. 2a = b + 2 D. 2a = b+ 63--R-2, b=-215. Given that (x + 2) is a factor of x³ – kx? + 2x + 7k, then the value of k isA. – 4-B. 4С.- 2D. 216. When x’ – px + q is divided by x2 – 3x + 2 the remainder is 4x – 1. The values of p and q are-A. p=3, q = 5 B. p 5, q= 3 C. p = -3. Q = 5 D. p = 3, q = -7%3D217. The equations ax² + 2x -1=0 and x² + 4x + a = 0 have a common root. The root value of ais :A. 0В. 1С. -3D. 318. The polynomial a' + b' + c' – 3abc has a factor:A. a-bB. a + b+ cС.а + сD. a -b- c|19. Given that xc is a factor of f (x) where f(x) = 2x3 – cx? + c(1 – c)x - (6 + c),|determine the possible values of cA. 2 or -3B. 2 or 3C. -2 or - 3D. -3 or 2|20. A polynomial p(x) leaves the remainder 2 and 5 when divided by (x- 2) and (x -3)|respectively. When p(x) is divided by (x – 2) (x – 3), the remainder isА. ЗхB. 4 - 3xС.О-D. 3x - 421. The roots of x- 7x- 6 = 0 areВ. -3, — 2, -122. When f (x) = 2x3 + x2 - 13x + 6 is divided by 2x - 1, the remainder isA. -2. -1,3C. -3, 1, 2D.-1C D.0A. 13В.52

Answered: Image /qna-images/answer/c1a442cc-d76e-47c7-8b0b-7c05648ed844.jpg

20. A polynomial p(x) leaves the remainder 2 and 5 when divided by (x- 2) and (x - 3) respectively. When p(x) is divided by (x- 2)(x - 3), the remainder is A. 3x B. 4 - 3x С.О D. 3x - 4 21. The roots of x3-7x-6= 0 are A. -2. -1,3 22. When f (x) = 2x + x2 – 13x + 6 is divided by 2x В. -3, -2, -1 C. -3, 1, 2 D.-1 1, the remainder is А. 13 В.52 D.0

20. A polynomial p(x) leaves the remainder 2 and 5 when divided by (x- 2) and (x - 3) respectively. When p(x) is divided by (x- 2)(x - 3), the remainder is A. 3x B. 4 - 3x С.О D. 3x - 4 21. The roots of x3-7x-6= 0 are A. -2. -1,3 22. When f (x) = 2x + x2 – 13x + 6 is divided by 2x В. -3, -2, -1 C. -3, 1, 2 D.-1 1, the remainder is А. 13 В.52 D.0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 26EQ

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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Question

Solve Q20, 21 & 22 showing clearly all steps involved

14. If x + 1 is a common factor of x³ – 3x + a and x* – 3x’– ax +b then
A. 2a = b B. b = 0C. 2a = b + 2 D. 2a = b+ 6
3
-
-
R-2, b=-2
15. Given that (x + 2) is a factor of x³ – kx? + 2x + 7k, then the value of k is
A. – 4
-
B. 4
С.- 2
D. 2
16. When x’ – px + q is divided by x2 – 3x + 2 the remainder is 4x – 1. The values of p and q are
-
A. p=3, q = 5 B. p 5, q= 3 C. p = -3. Q = 5 D. p = 3, q = -7
%3D
2
17. The equations ax² + 2x -1=0 and x² + 4x + a = 0 have a common root. The root value of a
is :
A. 0
В. 1
С. -3
D. 3
18. The polynomial a' + b' + c' – 3abc has a factor:
A. a-b
B. a + b+ c
С.а + с
D. a -b- c
|
19. Given that x
c is a factor of f (x) where f(x) = 2x3 – cx? + c(1 – c)x - (6 + c),
|
determine the possible values of c
A. 2 or -3
B. 2 or 3
C. -2 or - 3
D. -3 or 2
|
20. A polynomial p(x) leaves the remainder 2 and 5 when divided by (x- 2) and (x -3)
|
respectively. When p(x) is divided by (x – 2) (x – 3), the remainder is
А. Зх
B. 4 - 3x
С.О
-D. 3x - 4
21. The roots of x- 7x- 6 = 0 are
В. -3, — 2, -1
22. When f (x) = 2x3 + x2 - 13x + 6 is divided by 2x - 1, the remainder is
A. -2. -1,3
C. -3, 1, 2
D.-1
C D.0
A. 13
В.52

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