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If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is?
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If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then...
Understanding the Quadratic Polynomial
The given quadratic polynomial is:
2x² + 5x + 1
In a quadratic polynomial of the form ax² + bx + c, the sum of the roots (zeroes) can be determined using Vieta's formulas.
Identifying Coefficients
- a = 2 (coefficient of x²)
- b = 5 (coefficient of x)
- c = 1 (constant term)
Using Vieta's Formulas
According to Vieta's formulas, for a quadratic polynomial ax² + bx + c, the sum of the roots (alpha + beta) is given by:
alpha + beta = -b/a
Calculating the Sum of the Roots
Now, substituting the values of b and a:
- b = 5
- a = 2
So,
alpha + beta = -5/2
Final Result
Therefore, the sum of the zeroes (alpha + beta) of the polynomial 2x² + 5x + 1 is:
-2.5 or -5/2
This result clearly shows the relationship between the coefficients of the polynomial and its roots, providing a systematic way to find the sum of the zeroes.
The given quadratic polynomial is:
2x² + 5x + 1
In a quadratic polynomial of the form ax² + bx + c, the sum of the roots (zeroes) can be determined using Vieta's formulas.
Identifying Coefficients
- a = 2 (coefficient of x²)
- b = 5 (coefficient of x)
- c = 1 (constant term)
Using Vieta's Formulas
According to Vieta's formulas, for a quadratic polynomial ax² + bx + c, the sum of the roots (alpha + beta) is given by:
alpha + beta = -b/a
Calculating the Sum of the Roots
Now, substituting the values of b and a:
- b = 5
- a = 2
So,
alpha + beta = -5/2
Final Result
Therefore, the sum of the zeroes (alpha + beta) of the polynomial 2x² + 5x + 1 is:
-2.5 or -5/2
This result clearly shows the relationship between the coefficients of the polynomial and its roots, providing a systematic way to find the sum of the zeroes.
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If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is?
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If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is? 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 alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is?.
If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is? 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 alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is?.
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