UPSC Exam > UPSC Questions > If alpha and beeta are the zeroes of x2+x-2, ...
Start Learning for Free
If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta?
Most Upvoted Answer
If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + a...
Given information:
- Zeroes of the quadratic equation x² + x - 2 are alpha and beta.
Formula:
- If alpha and beta are the zeroes of a quadratic equation ax² + bx + c = 0, then the sum of the zeroes is -b/a and the product of the zeroes is c/a.
Finding the values of alpha and beta:
- In the given equation x² + x - 2 = 0, a = 1, b = 1, and c = -2.
- Sum of the zeroes (alpha + beta) = -b/a = -1/1 = -1.
- Product of the zeroes (alpha * beta) = c/a = -2/1 = -2.
- Therefore, alpha = 1 and beta = -2.
Calculating the required expression:
- We need to find alpha * beta² + alpha² * beta.
- Substituting the values of alpha and beta, we get:
- alpha * beta² + alpha² * beta
= 1 * (-2)² + 1² * (-2)
= 1 * 4 + 1 * (-2)
= 4 - 2
= 2.
Therefore, the value of alpha * beta² + alpha² * beta is 2.
- Zeroes of the quadratic equation x² + x - 2 are alpha and beta.
Formula:
- If alpha and beta are the zeroes of a quadratic equation ax² + bx + c = 0, then the sum of the zeroes is -b/a and the product of the zeroes is c/a.
Finding the values of alpha and beta:
- In the given equation x² + x - 2 = 0, a = 1, b = 1, and c = -2.
- Sum of the zeroes (alpha + beta) = -b/a = -1/1 = -1.
- Product of the zeroes (alpha * beta) = c/a = -2/1 = -2.
- Therefore, alpha = 1 and beta = -2.
Calculating the required expression:
- We need to find alpha * beta² + alpha² * beta.
- Substituting the values of alpha and beta, we get:
- alpha * beta² + alpha² * beta
= 1 * (-2)² + 1² * (-2)
= 1 * 4 + 1 * (-2)
= 4 - 2
= 2.
Therefore, the value of alpha * beta² + alpha² * beta is 2.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta?
Question Description
If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? 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 apha×beeta2 + alpha2 ×beeta? 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 apha×beeta2 + alpha2 ×beeta?.
If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? 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 apha×beeta2 + alpha2 ×beeta? 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 apha×beeta2 + alpha2 ×beeta?.
Solutions for If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? defined & explained in the simplest way possible. Besides giving the explanation of
If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta?, a detailed solution for If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? has been provided alongside types of If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? theory, EduRev gives you an
ample number of questions to practice If alpha and beeta are the zeroes of x2+x-2, then find apha×beeta2 + alpha2 ×beeta? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup