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If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta?
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsq...
Find 1/alpha + 1/beta
Understanding the given information:
- The quadratic polynomial given is p(x) = 2x^2 + 11x + 5
- Let alpha and beta be the zeroes of the polynomial p(x)
Sum of zeroes (alpha + beta) = -b/a
According to Vieta's formulas, the sum of the zeroes of a quadratic polynomial is given by -b/a, where a is the coefficient of x^2 and b is the coefficient of x in the polynomial.
In this case, a = 2 and b = 11. So, the sum of the zeroes (alpha + beta) = -11/2 = -5.5.
Product of zeroes (alpha * beta) = c/a
The product of the zeroes of a quadratic polynomial is given by c/a, where c is the constant term in the polynomial.
In this case, c = 5. So, the product of the zeroes (alpha * beta) = 5/2 = 2.5.
1/alpha + 1/beta = (alpha + beta) / (alpha * beta)
The expression 1/alpha + 1/beta can be written as (alpha + beta) / (alpha * beta) using the values of the sum and product of the zeroes calculated above.
Substitute the values, we get (-5.5) / 2.5 = -2.2.
Therefore, 1/alpha + 1/beta = -2.2.
Understanding the given information:
- The quadratic polynomial given is p(x) = 2x^2 + 11x + 5
- Let alpha and beta be the zeroes of the polynomial p(x)
Sum of zeroes (alpha + beta) = -b/a
According to Vieta's formulas, the sum of the zeroes of a quadratic polynomial is given by -b/a, where a is the coefficient of x^2 and b is the coefficient of x in the polynomial.
In this case, a = 2 and b = 11. So, the sum of the zeroes (alpha + beta) = -11/2 = -5.5.
Product of zeroes (alpha * beta) = c/a
The product of the zeroes of a quadratic polynomial is given by c/a, where c is the constant term in the polynomial.
In this case, c = 5. So, the product of the zeroes (alpha * beta) = 5/2 = 2.5.
1/alpha + 1/beta = (alpha + beta) / (alpha * beta)
The expression 1/alpha + 1/beta can be written as (alpha + beta) / (alpha * beta) using the values of the sum and product of the zeroes calculated above.
Substitute the values, we get (-5.5) / 2.5 = -2.2.
Therefore, 1/alpha + 1/beta = -2.2.
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta?
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta?.
If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta?.
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