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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...
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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.
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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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