**Solution:**

Let the root of the quadratic equation be *a* and *b*.

According to the given condition,

The quadratic equation is given by,

*x*^{2}– *x* (Sum of roots) + (Product of roots) = 0

*x*^{2} – *x* (*a* + *b*) + (*ab*) = 0

*x*^{2} – 16*x* + 25 = 0 [Using (1) and (2)]

Thus, the required quadratic equation is *x*^{2} – 16*x* + 25 = 0