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CASE STUDY QUESTION.
A mathematics teacher of class 10th write two different polynomials
f(x) = (3x²-5) (x²-3x+2) + k + 10
g(x) = 3x²-5 and ask some questions from students, then answer the following questions:
1. If f(x) is completely divisible by g(x), then find the value of k
4. Find the other two zeroes of f(x).?
CASE STUDY QUESTION.
A mathematics teacher of class 10th write two different polynomials
f(x) = (3x²-5) (x²-3x+2) + k + 10
g(x) = 3x²-5 and ask some questions from students, then answer the following questions:
1. If f(x) is completely divisible by g(x), then find the value of k
4. Find the other two zeroes of f(x).?
Most Upvoted Answer
2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two ...
1. Finding the Value of k
To determine the value of k for which f(x) is completely divisible by g(x), we start with the polynomials:
- f(x) = (3x² - 5)(x² - 3x + 2) + k + 10
- g(x) = 3x² - 5
For f(x) to be divisible by g(x), the remainder when f(x) is divided by g(x) must be zero.
1. Expand f(x):
- First, expand (3x² - 5)(x² - 3x + 2).
- This gives f(x) as a polynomial of degree 4.
2. Set the remainder to zero:
- For complete divisibility, the constant term after expansion and addition of k + 10 must equal zero when evaluated at the roots of g(x).
3. Find the roots of g(x):
- g(x) = 3x² - 5 = 0 leads to x² = 5/3.
- Roots are √(5/3) and -√(5/3).
4. Calculate f(√(5/3)) and set to zero:
- Substitute √(5/3) into f(x) and solve for k. This will yield the value of k.
2. Finding the Other Two Zeroes of f(x)
Once k is determined, we can find the other two zeroes of f(x).
1. Express f(x) with k:
- Substitute the found k back into f(x) to get the complete polynomial.
2. Use the Factor Theorem:
- Since g(x) is a factor, we can express f(x) as g(x)(Ax² + Bx + C) for some constants A, B, and C.
3. Find the Quadratic:
- Expand and equate coefficients to find A, B, and C.
4. Solve for Zeroes:
- Use the quadratic formula to find the other two zeroes from the quadratic expression.
By following these steps, the complete polynomial function and its roots can be accurately determined.
To determine the value of k for which f(x) is completely divisible by g(x), we start with the polynomials:
- f(x) = (3x² - 5)(x² - 3x + 2) + k + 10
- g(x) = 3x² - 5
For f(x) to be divisible by g(x), the remainder when f(x) is divided by g(x) must be zero.
1. Expand f(x):
- First, expand (3x² - 5)(x² - 3x + 2).
- This gives f(x) as a polynomial of degree 4.
2. Set the remainder to zero:
- For complete divisibility, the constant term after expansion and addition of k + 10 must equal zero when evaluated at the roots of g(x).
3. Find the roots of g(x):
- g(x) = 3x² - 5 = 0 leads to x² = 5/3.
- Roots are √(5/3) and -√(5/3).
4. Calculate f(√(5/3)) and set to zero:
- Substitute √(5/3) into f(x) and solve for k. This will yield the value of k.
2. Finding the Other Two Zeroes of f(x)
Once k is determined, we can find the other two zeroes of f(x).
1. Express f(x) with k:
- Substitute the found k back into f(x) to get the complete polynomial.
2. Use the Factor Theorem:
- Since g(x) is a factor, we can express f(x) as g(x)(Ax² + Bx + C) for some constants A, B, and C.
3. Find the Quadratic:
- Expand and equate coefficients to find A, B, and C.
4. Solve for Zeroes:
- Use the quadratic formula to find the other two zeroes from the quadratic expression.
By following these steps, the complete polynomial function and its roots can be accurately determined.
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2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).?
Question Description
2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).?.
2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).?.
Solutions for 2+8xCASE STUDY QUESTION.A mathematics teacher of class 10th write two different polynomialsf(x) = (3x²-5) (x²-3x+2) + k + 10g(x) = 3x²-5 and ask some questions from students, then answer the following questions:1. If f(x) is completely divisible by g(x), then find the value of k4. Find the other two zeroes of f(x).? in English & in Hindi are available as part of our courses for UPSC.
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