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Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros?
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Find a quadratic polynomial, the sum and product of whose zeroes are 6...
Quadratic Polynomial with Sum and Product of Zeroes
- Let's assume the quadratic polynomial as ax^2 + bx + c.
- According to the given conditions, the sum of the zeroes is 6 and the product of the zeroes is 9.
- By Vieta's formulas, the sum of the zeroes is -b/a and the product of the zeroes is c/a.
Finding the Quadratic Polynomial
- We know that the sum of the zeroes is 6 and the product of the zeroes is 9.
- So, we can write two equations based on the given conditions:
1. -b/a = 6
2. c/a = 9
- From the first equation, we get: b = -6a
- Substituting this value of b in the quadratic polynomial, we get: ax^2 - 6ax + c
- Now, from the second equation, we get: c = 9a
- Substituting this value of c in the quadratic polynomial, we get: ax^2 - 6ax + 9a
- Factoring out 'a', we get: a(x^2 - 6x + 9)
- Further simplifying, we get: a(x - 3)^2
Finding the Zeroes
- Setting the quadratic polynomial to zero, we get: a(x - 3)^2 = 0
- This implies that the zeroes are x = 3.
Conclusion
- Therefore, the quadratic polynomial with sum and product of zeroes as 6 and 9 respectively is a(x - 3)^2, and the zeroes are 3.
- Let's assume the quadratic polynomial as ax^2 + bx + c.
- According to the given conditions, the sum of the zeroes is 6 and the product of the zeroes is 9.
- By Vieta's formulas, the sum of the zeroes is -b/a and the product of the zeroes is c/a.
Finding the Quadratic Polynomial
- We know that the sum of the zeroes is 6 and the product of the zeroes is 9.
- So, we can write two equations based on the given conditions:
1. -b/a = 6
2. c/a = 9
- From the first equation, we get: b = -6a
- Substituting this value of b in the quadratic polynomial, we get: ax^2 - 6ax + c
- Now, from the second equation, we get: c = 9a
- Substituting this value of c in the quadratic polynomial, we get: ax^2 - 6ax + 9a
- Factoring out 'a', we get: a(x^2 - 6x + 9)
- Further simplifying, we get: a(x - 3)^2
Finding the Zeroes
- Setting the quadratic polynomial to zero, we get: a(x - 3)^2 = 0
- This implies that the zeroes are x = 3.
Conclusion
- Therefore, the quadratic polynomial with sum and product of zeroes as 6 and 9 respectively is a(x - 3)^2, and the zeroes are 3.
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Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros?
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Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros? 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 Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros?.
Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros? 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 Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively hence find the zeros?.
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