269. Quickly write two quadratic equations with one unknown of the form $x^{2}+p x+q=0$, having one and only one common root.
269. Think of a certain number as the common root of these equations, for example, 2, and write the equations, using arbitrary (different) coefficients of the linear terms and selecting the terms free from $\boldsymbol{x}$ accordingly so that the trinomials become zero. That the second roots are not identical follows at least from the fact that the known terms, representing in each equation the product of its roots, are not the same. Otherwise: write $(x-2)(x+3)=0$ and $(x-2)(x-5)=0$ and perform the multiplications.