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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?
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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.
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If (x + 2) and (x – 1) are the factors of (x3+ 10x2+ mx + n), th...
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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?
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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?.
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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
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