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If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)?
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If a and b are zeroes of the polynomial x2-x-6 then find a quadratic p...
Quadratic Polynomial with given zeroes
- Given zeroes of the polynomial x^2-x-6 are a and b.
- We need to find a quadratic polynomial with zeroes (3a+2b) and (2a+3b).
Sum and Product of Zeroes
- For a quadratic polynomial ax^2 + bx + c, the sum of zeroes is given by -b/a and the product of zeroes is given by c/a.
Finding Sum and Product of Zeroes
- Sum of zeroes: a + b = -(-1) = 1
- Product of zeroes: ab = -6
Finding the Quadratic Polynomial
- The required quadratic polynomial with zeroes (3a+2b) and (2a+3b) can be written as:
- (x - (3a+2b))(x - (2a+3b)) = 0
- Expanding this equation, we get:
- x^2 - (3a+2b + 2a+3b)x + (3a+2b)(2a+3b) = 0
- Simplifying further, we get:
- x^2 - (5a+5b)x + (6a^2 + 13ab + 6b^2) = 0
Final Quadratic Polynomial
- Therefore, the quadratic polynomial with zeroes (3a+2b) and (2a+3b) is:
- x^2 - (5a+5b)x + (6a^2 + 13ab + 6b^2) = 0
- Given zeroes of the polynomial x^2-x-6 are a and b.
- We need to find a quadratic polynomial with zeroes (3a+2b) and (2a+3b).
Sum and Product of Zeroes
- For a quadratic polynomial ax^2 + bx + c, the sum of zeroes is given by -b/a and the product of zeroes is given by c/a.
Finding Sum and Product of Zeroes
- Sum of zeroes: a + b = -(-1) = 1
- Product of zeroes: ab = -6
Finding the Quadratic Polynomial
- The required quadratic polynomial with zeroes (3a+2b) and (2a+3b) can be written as:
- (x - (3a+2b))(x - (2a+3b)) = 0
- Expanding this equation, we get:
- x^2 - (3a+2b + 2a+3b)x + (3a+2b)(2a+3b) = 0
- Simplifying further, we get:
- x^2 - (5a+5b)x + (6a^2 + 13ab + 6b^2) = 0
Final Quadratic Polynomial
- Therefore, the quadratic polynomial with zeroes (3a+2b) and (2a+3b) is:
- x^2 - (5a+5b)x + (6a^2 + 13ab + 6b^2) = 0
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If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)?
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If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)? 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 If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)?.
If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)? 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 If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are zeroes of the polynomial x2-x-6 then find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)?.
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