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Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3?
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Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3?
Forming a Quadratic Polynomial with Given Zeroes
To form a quadratic polynomial with the given zeroes of 2+√3 and 2-√3, we can use the fact that the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0 are related to the coefficients b and c.
Sum and Product of Zeroes
The sum of the zeroes in this case would be:
(2+√3) + (2-√3) = 4
The product of the zeroes would be:
(2+√3)(2-√3) = 4 - 3 = 1
Forming the Quadratic Polynomial
Using the sum and product of the zeroes, we can write the quadratic polynomial as:
(x - (2+√3))(x - (2-√3)) = 0
Expanding this expression, we get:
x^2 - 4x + 1 = 0
Therefore, the quadratic polynomial with the zeroes 2+√3 and 2-√3 is:
x^2 - 4x + 1 = 0
To form a quadratic polynomial with the given zeroes of 2+√3 and 2-√3, we can use the fact that the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0 are related to the coefficients b and c.
Sum and Product of Zeroes
The sum of the zeroes in this case would be:
(2+√3) + (2-√3) = 4
The product of the zeroes would be:
(2+√3)(2-√3) = 4 - 3 = 1
Forming the Quadratic Polynomial
Using the sum and product of the zeroes, we can write the quadratic polynomial as:
(x - (2+√3))(x - (2-√3)) = 0
Expanding this expression, we get:
x^2 - 4x + 1 = 0
Therefore, the quadratic polynomial with the zeroes 2+√3 and 2-√3 is:
x^2 - 4x + 1 = 0
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Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3?
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Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3?.
Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Frame a quadratic polynomial whose zeroes are 2+ root 3 and 2-root 3?.
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