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).
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