Class 11 Exam > Class 11 Questions > If alpha and beta are the roots of the equati...
Start Learning for Free
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ?
Most Upvoted Answer
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation...
Community Answer
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation...
Transformation of Roots
- Given roots of the equation 6x²-x-2=0 are alpha and beta.
- Let's find the sum and product of the roots using Vieta's formulas.
- Sum of roots (alpha + beta) = -(-1)/6 = 1/6
- Product of roots (alpha * beta) = -2/6 = -1/3
Finding New Roots
- We are asked to find the equation with roots alpha²/2 and beta²/2.
- Let's find the new roots by squaring the given roots and dividing by 2.
- New root 1 = (alpha²)/2 = (alpha * alpha)/2 = alpha²/2
- New root 2 = (beta²)/2 = (beta * beta)/2 = beta²/2
Forming New Equation
- The new equation with roots alpha²/2 and beta²/2 can be written as:
- x² - (sum of roots)*(x) + product of roots = 0
- x² - (1/6)x - 1/3 = 0
- Multiplying by 6 to clear fractions, we get:
- 6x² - x - 2 = 0
Therefore, the equation whose roots are alpha²/2 and beta²/2 is 6x² - x - 2 = 0.
- Given roots of the equation 6x²-x-2=0 are alpha and beta.
- Let's find the sum and product of the roots using Vieta's formulas.
- Sum of roots (alpha + beta) = -(-1)/6 = 1/6
- Product of roots (alpha * beta) = -2/6 = -1/3
Finding New Roots
- We are asked to find the equation with roots alpha²/2 and beta²/2.
- Let's find the new roots by squaring the given roots and dividing by 2.
- New root 1 = (alpha²)/2 = (alpha * alpha)/2 = alpha²/2
- New root 2 = (beta²)/2 = (beta * beta)/2 = beta²/2
Forming New Equation
- The new equation with roots alpha²/2 and beta²/2 can be written as:
- x² - (sum of roots)*(x) + product of roots = 0
- x² - (1/6)x - 1/3 = 0
- Multiplying by 6 to clear fractions, we get:
- 6x² - x - 2 = 0
Therefore, the equation whose roots are alpha²/2 and beta²/2 is 6x² - x - 2 = 0.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ?
Question Description
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ?.
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ?.
Solutions for If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? defined & explained in the simplest way possible. Besides giving the explanation of
If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ?, a detailed solution for If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? has been provided alongside types of If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? theory, EduRev gives you an
ample number of questions to practice If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 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