Two consecutive positive odd numbers are such that the sum of their squares is 130. Formulate the quadratic equation whose roots are these numbers. 

Let two consecutive positive odd numbers be x and x + 2.

Sum the square of the numbers $\begin{array}{r}={\mathrm{x}}^2+(\mathrm{x}+2{)}^2\end{array}$

It is given that the sum is 130. Therefore,

$\begin{array}{rl}{\mathrm{x}}^2+(\mathrm{x}+2{)}^2& \mathrm{ }=130\\ {\mathrm{x}}^2+{\mathrm{x}}^2+4\mathrm{x}+4& \mathrm{ }=130\\ 2{\mathrm{x}}^2+4\mathrm{x}-126& \mathrm{ }=0\\ {\mathrm{x}}^2+2\mathrm{x}-63& \mathrm{ }=0\end{array}$

This is the required quadratic equation.