iran-konkur 2013 Q105

iran-konkur · Other · konkur-riazi_1392 Roots of polynomials Vieta's formulas: compute symmetric functions of roots
105- If $\alpha, \beta$ are the roots of the equation $2x^2 - 3x - 4 = 0$, the equation whose roots are $\left\{\dfrac{1}{\alpha}+1,\ \dfrac{1}{\beta}+1\right\}$ is:
  • [(1)] $4x^2 - \Delta x + 1 = 0$
  • [(2)] $4x^2 - 3x + 1 = 0$
  • [(3)] $4x^2 - \Delta x - 1 = 0$
  • [(4)] $4x^2 - 3x - 1 = 0$
\textbf{105-} If $\alpha, \beta$ are the roots of the equation $2x^2 - 3x - 4 = 0$, the equation whose roots are $\left\{\dfrac{1}{\alpha}+1,\ \dfrac{1}{\beta}+1\right\}$ is:

\begin{itemize}
\item[(1)] $4x^2 - \Delta x + 1 = 0$
\item[(2)] $4x^2 - 3x + 1 = 0$
\item[(3)] $4x^2 - \Delta x - 1 = 0$
\item[(4)] $4x^2 - 3x - 1 = 0$
\end{itemize}