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T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient?
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Quadratic Polynomial: Finding Zeroes and Relationship with Coefficients
Finding Zeroes of the Quadratic Polynomial:
- Given polynomial: T^2 - √15
- To find the zeroes, set the polynomial equal to zero: T^2 - √15 = 0
- Solve for T: T = ±√15
Verifying Relationship between Zeroes and Coefficients:
- The general form of a quadratic polynomial is ax^2 + bx + c.
- The sum of the zeroes of a quadratic polynomial is given by -b/a and the product of the zeroes is given by c/a.
- In this case, the coefficients of the polynomial are a = 1, b = 0, and c = -√15.
- The sum of the zeroes is -b/a = 0/1 = 0.
- The product of the zeroes is c/a = -√15/1 = -√15.
Explanation:
- The zeroes of the quadratic polynomial T^2 - √15 are ±√15.
- The relationship between the zeroes and the coefficients is verified by calculating the sum and product of the zeroes using the formulas -b/a and c/a.
- The sum of the zeroes is 0 and the product of the zeroes is -√15, which aligns with the relationship between the zeroes and coefficients of a quadratic polynomial.
- This demonstrates the connection between the zeroes of a polynomial and its coefficients in the context of the given quadratic polynomial.
Finding Zeroes of the Quadratic Polynomial:
- Given polynomial: T^2 - √15
- To find the zeroes, set the polynomial equal to zero: T^2 - √15 = 0
- Solve for T: T = ±√15
Verifying Relationship between Zeroes and Coefficients:
- The general form of a quadratic polynomial is ax^2 + bx + c.
- The sum of the zeroes of a quadratic polynomial is given by -b/a and the product of the zeroes is given by c/a.
- In this case, the coefficients of the polynomial are a = 1, b = 0, and c = -√15.
- The sum of the zeroes is -b/a = 0/1 = 0.
- The product of the zeroes is c/a = -√15/1 = -√15.
Explanation:
- The zeroes of the quadratic polynomial T^2 - √15 are ±√15.
- The relationship between the zeroes and the coefficients is verified by calculating the sum and product of the zeroes using the formulas -b/a and c/a.
- The sum of the zeroes is 0 and the product of the zeroes is -√15, which aligns with the relationship between the zeroes and coefficients of a quadratic polynomial.
- This demonstrates the connection between the zeroes of a polynomial and its coefficients in the context of the given quadratic polynomial.
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T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient?
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T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient?.
T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for T^2-√15 .find the zeroes of the quadratic polynomial and verify the relationship between zeroes and coefficient?.
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