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If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta?
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If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + al...
Given Information:
- Zeroes of the quadratic equation x^2 + x - 2 are alpha and beta.
Formula:
- Sum of zeroes (alpha + beta) = -b/a
- Product of zeroes (alpha * beta) = c/a
Calculation:
- In this case, a = 1, b = 1, and c = -2 from the given quadratic equation x^2 + x - 2.
Finding the Sum and Product of Zeroes:
- Sum of zeroes (alpha + beta) = -b/a = -1/1 = -1
- Product of zeroes (alpha * beta) = c/a = -2/1 = -2
Finding the Required Expression:
- We need to find alpha^2 * beta + alpha * beta^2.
- By expanding this expression, we get alpha^2 * beta + alpha * beta^2 = alpha * beta * (alpha + beta).
- Substituting the values of alpha + beta and alpha * beta, we get alpha^2 * beta + alpha * beta^2 = -2 * -1 = 2.
Final Answer:
- Therefore, aphabeeta^2 + alpha^2beeta = 2.
- Zeroes of the quadratic equation x^2 + x - 2 are alpha and beta.
Formula:
- Sum of zeroes (alpha + beta) = -b/a
- Product of zeroes (alpha * beta) = c/a
Calculation:
- In this case, a = 1, b = 1, and c = -2 from the given quadratic equation x^2 + x - 2.
Finding the Sum and Product of Zeroes:
- Sum of zeroes (alpha + beta) = -b/a = -1/1 = -1
- Product of zeroes (alpha * beta) = c/a = -2/1 = -2
Finding the Required Expression:
- We need to find alpha^2 * beta + alpha * beta^2.
- By expanding this expression, we get alpha^2 * beta + alpha * beta^2 = alpha * beta * (alpha + beta).
- Substituting the values of alpha + beta and alpha * beta, we get alpha^2 * beta + alpha * beta^2 = -2 * -1 = 2.
Final Answer:
- Therefore, aphabeeta^2 + alpha^2beeta = 2.
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If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta?
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If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta? 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 beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta?.
If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta? 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 beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beeta are the zeroes of x2+x-2, then find aphabeeta2 + alpha2beeta?.
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