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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-2alphabeta?
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsq...
Given Information:
The quadratic polynomial is p(x) = 2x^2 + 11x + 5
The zeroes of the polynomial are alpha and beta
Formula:
If alpha and beta are the zeroes of a quadratic polynomial ax^2 + bx + c, then:
1/alpha + 1/beta = (alpha + beta) / (alpha * beta)
2alpha * beta = c / a
Solution:
Finding Sum and Product of Zeroes:
From the given polynomial, a = 2, b = 11, and c = 5
Sum of zeroes, alpha + beta = -b/a = -11/2
Product of zeroes, alpha * beta = c/a = 5/2
Calculating 1/alpha + 1/beta - 2alpha*beta:
1/alpha + 1/beta = (alpha + beta) / (alpha * beta)
= (-11/2) / (5/2)
= -11/5
2alpha*beta = c / a = 5/2
Therefore, 1/alpha + 1/beta - 2alpha*beta = -11/5 - 5/2
= (-11*2 - 5*5) / 5*2
= (-22 - 25) / 10
= -47/10
Hence, 1/alpha + 1/beta - 2alpha*beta = -47/10
The quadratic polynomial is p(x) = 2x^2 + 11x + 5
The zeroes of the polynomial are alpha and beta
Formula:
If alpha and beta are the zeroes of a quadratic polynomial ax^2 + bx + c, then:
1/alpha + 1/beta = (alpha + beta) / (alpha * beta)
2alpha * beta = c / a
Solution:
Finding Sum and Product of Zeroes:
From the given polynomial, a = 2, b = 11, and c = 5
Sum of zeroes, alpha + beta = -b/a = -11/2
Product of zeroes, alpha * beta = c/a = 5/2
Calculating 1/alpha + 1/beta - 2alpha*beta:
1/alpha + 1/beta = (alpha + beta) / (alpha * beta)
= (-11/2) / (5/2)
= -11/5
2alpha*beta = c / a = 5/2
Therefore, 1/alpha + 1/beta - 2alpha*beta = -11/5 - 5/2
= (-11*2 - 5*5) / 5*2
= (-22 - 25) / 10
= -47/10
Hence, 1/alpha + 1/beta - 2alpha*beta = -47/10
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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-2alphabeta?
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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-2alphabeta? 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-2alphabeta? 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-2alphabeta?.
If alpha and beta are the zeroes of the quadratic polynomial p(x)=2xsquare+11x+5 then find 1/alpha+1/beta-2alphabeta? 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-2alphabeta? 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-2alphabeta?.
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