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If alpha and beta are the roots of the equation 6x²-x-2=0 the equation whose roots are alpha² 2,beta² 2, is ?
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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.
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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 2025 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 2025 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 2025 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 2025 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 ?.
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