To find an equation whose roots are a transformation of the roots of a given equation, substitute the relationship between the new roots and the old roots into the original equation. If the roots are $x_i$ and the new roots are $y_i = f(x_i)$, then express $x_i$ in terms of $y_i$, i.e., $x_i = f^{-1}(y_i)$, and substitute this into the original polynomial.
If $\alpha, \beta, \gamma$ are the roots of the equation $8x^3-4x^2+6x-1=0$, then equation having roots $\alpha+\frac{1}{2}, \beta+ \frac{1}{2}, \gamma+\frac{1}{2}$ is - - Question not attempted
Asked in Asst. Statistical Officer (Agri. Deptt.) 2024 · Topic: Mechanics (Lagrangian Formulation (Generalized Coordinates, Euler-Lagrange Equations))
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