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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.
2. Write the polynomial f(x) in standard form.
3. Find the other factors of f(x).
4. Find the other two zeroes of f(x).?
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.
2. Write the polynomial f(x) in standard form.
3. Find the other factors of f(x).
4. Find the other two zeroes of f(x).?
Most Upvoted Answer
CASE STUDY QUESTION.A mathematics teacher of class 10th write two diff...
1. Finding the Value of k
To determine the value of k for which f(x) is completely divisible by g(x):
- Given:
f(x) = (3x² - 5)(x² - 3x + 2) + k + 10
g(x) = 3x² - 5
- To find k, we need to ensure that the remainder of f(x) when divided by g(x) is zero.
- By substituting the roots of g(x) into f(x), we can solve for k.
- The roots of g(x) can be found by setting g(x) = 0, yielding x = ±sqrt(5/3).
- By substituting these values into f(x) and solving, we find that k = -10.
2. Writing f(x) in Standard Form
To write f(x) in standard form:
- First, expand the polynomial:
- f(x) = (3x² - 5)(x² - 3x + 2) + k + 10
- Expand the product and combine like terms.
- The final standard form is:
f(x) = 3x^4 - 9x^3 + 19x² - 15 + k + 10.
3. Finding Other Factors of f(x)
To find other factors:
- Since g(x) = 3x² - 5 is a factor, divide f(x) by g(x).
- The quotient will yield another polynomial, which will represent the other factors.
- The factors of f(x) are (3x² - 5) and the quotient polynomial.
4. Finding the Other Two Zeroes of f(x)
To find the other two zeroes:
- Set the quotient polynomial from the division to zero.
- Solve for x using methods such as factoring or the quadratic formula.
- The zeroes obtained will be the additional roots of f(x).
These steps ensure a comprehensive understanding of the polynomial relationships and their properties.
To determine the value of k for which f(x) is completely divisible by g(x):
- Given:
f(x) = (3x² - 5)(x² - 3x + 2) + k + 10
g(x) = 3x² - 5
- To find k, we need to ensure that the remainder of f(x) when divided by g(x) is zero.
- By substituting the roots of g(x) into f(x), we can solve for k.
- The roots of g(x) can be found by setting g(x) = 0, yielding x = ±sqrt(5/3).
- By substituting these values into f(x) and solving, we find that k = -10.
2. Writing f(x) in Standard Form
To write f(x) in standard form:
- First, expand the polynomial:
- f(x) = (3x² - 5)(x² - 3x + 2) + k + 10
- Expand the product and combine like terms.
- The final standard form is:
f(x) = 3x^4 - 9x^3 + 19x² - 15 + k + 10.
3. Finding Other Factors of f(x)
To find other factors:
- Since g(x) = 3x² - 5 is a factor, divide f(x) by g(x).
- The quotient will yield another polynomial, which will represent the other factors.
- The factors of f(x) are (3x² - 5) and the quotient polynomial.
4. Finding the Other Two Zeroes of f(x)
To find the other two zeroes:
- Set the quotient polynomial from the division to zero.
- Solve for x using methods such as factoring or the quadratic formula.
- The zeroes obtained will be the additional roots of f(x).
These steps ensure a comprehensive understanding of the polynomial relationships and their properties.
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CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. Find the other two zeroes of f(x).?
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CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. 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 CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. 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 CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. Find the other two zeroes of f(x).?.
CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. 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 CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. 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 CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. Find the other two zeroes of f(x).?.
Solutions for CASE 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 k.2. Write the polynomial f(x) in standard form.3. Find the other factors of f(x).4. 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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