Class 9 Exam > Class 9 Questions > If (x + 2) and (x – 1) are the factors ...
Start Learning for Free
If (x + 2) and (x – 1) are the factors of (x3 + 10x2 + mx + n), the values of m and n are :-
- a)m = 5, n = –3
- b)m = 17, n = –8
- c)m = 7, n = –18
- d)m = 23, n = –19
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), th...
There are a few different ways to approach this problem, but one common method is to use the fact that if two expressions are equal, then their squares are equal as well. So, we can start by squaring both sides of each inequality:
(x - 2)^2 < />
(x + 2)^2 > 36
Expanding the squares gives:
x^2 - 4x + 4 < />
x^2 + 4x + 4 > 36
Simplifying each inequality by subtracting or adding constants and collecting like terms gives:
x^2 - 4x - 21 < />
x^2 + 4x - 32 > 0
To solve these inequalities, we can use a sign chart or factor the quadratic expressions. Factoring gives:
x^2 - 4x - 21 < />
(x - 7)(x + 3) < />
The roots of this inequality are x = -3 and x = 7, so we can test intervals of x to see when the expression is negative:
x < -3:="" (-)(-)="" />< 0,="" />
-3 < x="" />< 7:="" (+)(-)="" />< 0,="" />
x > 7: (+)(+) < 0,="" />
Therefore, the solution to the first inequality is:
-3 < x="" />< />
Similarly, factoring the second inequality gives:
x^2 + 4x - 32 > 0
(x - 4)(x + 8) > 0
The roots of this inequality are x = -8 and x = 4, so we can again test intervals of x:
x < -8:="" (-)(-)="" /> 0, true
-8 < x="" />< 4:="" (+)(-)="" /> 0, false
x > 4: (+)(+) > 0, true
Therefore, the solution to the second inequality is:
x < -8="" or="" x="" /> 4
Putting these solutions together, we have:
-8 < x="" />< 7="" or="" x="" /> 4
This is the final solution to the system of inequalities.
(x - 2)^2 < />
(x + 2)^2 > 36
Expanding the squares gives:
x^2 - 4x + 4 < />
x^2 + 4x + 4 > 36
Simplifying each inequality by subtracting or adding constants and collecting like terms gives:
x^2 - 4x - 21 < />
x^2 + 4x - 32 > 0
To solve these inequalities, we can use a sign chart or factor the quadratic expressions. Factoring gives:
x^2 - 4x - 21 < />
(x - 7)(x + 3) < />
The roots of this inequality are x = -3 and x = 7, so we can test intervals of x to see when the expression is negative:
x < -3:="" (-)(-)="" />< 0,="" />
-3 < x="" />< 7:="" (+)(-)="" />< 0,="" />
x > 7: (+)(+) < 0,="" />
Therefore, the solution to the first inequality is:
-3 < x="" />< />
Similarly, factoring the second inequality gives:
x^2 + 4x - 32 > 0
(x - 4)(x + 8) > 0
The roots of this inequality are x = -8 and x = 4, so we can again test intervals of x:
x < -8:="" (-)(-)="" /> 0, true
-8 < x="" />< 4:="" (+)(-)="" /> 0, false
x > 4: (+)(+) > 0, true
Therefore, the solution to the second inequality is:
x < -8="" or="" x="" /> 4
Putting these solutions together, we have:
-8 < x="" />< 7="" or="" x="" /> 4
This is the final solution to the system of inequalities.
Free Test
FREE
| Start Free Test |
Community Answer
If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), th...
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Top Courses for Class 9View all
If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer?
Question Description
If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer?.
If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer?.
Solutions for If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), the values of m and n are :-a)m = 5, n = –3b)m = 17, n = –8c)m = 7, n = –18d)m = 23, n = –19Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup