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find the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2
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Finding zeroes of polynomial
To find the zeroes of the given polynomial, we need to set the polynomial equal to zero and solve for x.
x² - √2x + √2 = 0
Using the quadratic formula, we can solve for x:
x = [-(-√2) ± √((-√2)² - 4(1)(√2))] / 2(1)
Simplifying, we get:
x = (√2 ± √2) / 2
Therefore, the zeroes of the polynomial are:
x₁ = (√2 + √2) / 2 = √2
x₂ = (√2 - √2) / 2 = 0
Verifying relationship between zeroes and coefficients of polynomial
The relationship between the zeroes and coefficients of a polynomial is given by Vieta's formulas. For a quadratic polynomial of the form ax² + bx + c, the sum of the zeroes is -b/a and the product of the zeroes is c/a.
In this case, our polynomial is x² - √2x + √2, so a = 1, b = -√2, and c = √2.
Using Vieta's formulas, we can verify the relationship between the zeroes and coefficients:
Sum of zeroes = -b/a = -(-√2) / 1 = √2
Product of zeroes = c/a = √2 / 1 = √2
Therefore, we have verified that the sum of the zeroes is equal to the coefficient of x divided by the leading coefficient, and the product of the zeroes is equal to the constant coefficient divided by the leading coefficient.
To find the zeroes of the given polynomial, we need to set the polynomial equal to zero and solve for x.
x² - √2x + √2 = 0
Using the quadratic formula, we can solve for x:
x = [-(-√2) ± √((-√2)² - 4(1)(√2))] / 2(1)
Simplifying, we get:
x = (√2 ± √2) / 2
Therefore, the zeroes of the polynomial are:
x₁ = (√2 + √2) / 2 = √2
x₂ = (√2 - √2) / 2 = 0
Verifying relationship between zeroes and coefficients of polynomial
The relationship between the zeroes and coefficients of a polynomial is given by Vieta's formulas. For a quadratic polynomial of the form ax² + bx + c, the sum of the zeroes is -b/a and the product of the zeroes is c/a.
In this case, our polynomial is x² - √2x + √2, so a = 1, b = -√2, and c = √2.
Using Vieta's formulas, we can verify the relationship between the zeroes and coefficients:
Sum of zeroes = -b/a = -(-√2) / 1 = √2
Product of zeroes = c/a = √2 / 1 = √2
Therefore, we have verified that the sum of the zeroes is equal to the coefficient of x divided by the leading coefficient, and the product of the zeroes is equal to the constant coefficient divided by the leading coefficient.
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find the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2
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find the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2 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 the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2 covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2.
find the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2 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 the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2 covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the zeroes of polynomial and verify relationship between zeroes and coefficient of polynomial x2 -(root2+1)x+root2.
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