Option A: $7x^2 - 50x + 7 = 0$
Sum of roots $= 7 + \dfrac{1}{7} = \dfrac{50}{7}$; Product of roots $= 7 \times \dfrac{1}{7} = 1$.
Required equation: $x^2 - \dfrac{50}{7}x + 1 = 0$, i.e., $7x^2 - 50x + 7 = 0$.
For any quadratic with roots $\alpha$ and $\beta$: equation is $x^2 - (\alpha+\beta)x + \alpha\beta = 0$. Multiply through by 7 to clear the fraction. Key check: product of roots = 1 (not $\frac{1}{7}$), which rules out options B, C, D immediately.