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Read the following text and answer the following questions on the basis of the same:
A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.
Q. Nature of roots of the above quadratic equation are:
- a)Real and Equal
- b)Unreal
- c)Real and Unequal
- d)None
Correct answer is option 'C'. Can you explain this answer?
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Read the following text and answer the following questions on the bas...
We can see, the discriminant of the given quadratic equation is positive but not a perfect square. Hence, the roots of a quadratic equation are real, unequal.
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Read the following text and answer the following questions on the bas...
Given:
- A small scale industry produces a certain number of boxes of candles in a day.
- Number of boxes prepared by each worker on a particular day was 2 more than thrice the number of workers working in the industry.
- The number of boxes produced in a particular day was 85.
To find:
The nature of roots of the quadratic equation.
Solution:
Let's assume the number of workers in the industry as 'x'.
According to the given information, the number of boxes prepared by each worker on that day was 2 more than thrice the number of workers. Therefore, the number of boxes prepared by each worker can be represented as 3x + 2.
The total number of boxes produced in a day can be calculated by multiplying the number of boxes prepared by each worker by the number of workers:
Total number of boxes = (3x + 2) * x
We know that the total number of boxes produced in a particular day was 85:
(3x + 2) * x = 85
Now, let's solve this equation to find the nature of its roots.
Step 1: Convert the equation into standard quadratic form: ax^2 + bx + c = 0
3x^2 + 2x - 85 = 0
Step 2: Calculate the discriminant (D) using the formula: D = b^2 - 4ac
D = (2)^2 - 4(3)(-85)
D = 4 + 1020
D = 1024
Step 3: Determine the nature of roots based on the value of the discriminant:
- If D > 0, the roots are real and unequal.
- If D = 0, the roots are real and equal.
- If D < 0,="" the="" roots="" are="" />
In this case, D = 1024, which is greater than 0. Therefore, the nature of roots of the quadratic equation is real and unequal (option C).
- A small scale industry produces a certain number of boxes of candles in a day.
- Number of boxes prepared by each worker on a particular day was 2 more than thrice the number of workers working in the industry.
- The number of boxes produced in a particular day was 85.
To find:
The nature of roots of the quadratic equation.
Solution:
Let's assume the number of workers in the industry as 'x'.
According to the given information, the number of boxes prepared by each worker on that day was 2 more than thrice the number of workers. Therefore, the number of boxes prepared by each worker can be represented as 3x + 2.
The total number of boxes produced in a day can be calculated by multiplying the number of boxes prepared by each worker by the number of workers:
Total number of boxes = (3x + 2) * x
We know that the total number of boxes produced in a particular day was 85:
(3x + 2) * x = 85
Now, let's solve this equation to find the nature of its roots.
Step 1: Convert the equation into standard quadratic form: ax^2 + bx + c = 0
3x^2 + 2x - 85 = 0
Step 2: Calculate the discriminant (D) using the formula: D = b^2 - 4ac
D = (2)^2 - 4(3)(-85)
D = 4 + 1020
D = 1024
Step 3: Determine the nature of roots based on the value of the discriminant:
- If D > 0, the roots are real and unequal.
- If D = 0, the roots are real and equal.
- If D < 0,="" the="" roots="" are="" />
In this case, D = 1024, which is greater than 0. Therefore, the nature of roots of the quadratic equation is real and unequal (option C).
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Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer?
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Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer?.
Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Nature of roots of the above quadratic equation are:a)Real and Equalb)Unrealc)Real and Unequald)NoneCorrect answer is option 'C'. Can you explain this answer?.
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