b) Determine the mean, c) find the range, d) state the modal mark. 5) The sum of two numbers is 20 and their product is 77. a) Form a quadratic equation whose roots are the numbers. b) Solve the equation. c) Hence find the two numbers.

Let the two numbers be $x_1$ and $x_2$.
We are given the product: $x_1 \cdot x_2 = 77$.
We assume the sum: $x_1 + x_2 = 18$.

A quadratic equation with roots $x_1$ and $x_2$ can be written in the form:

Substitute the sum and product into the equation.

The quadratic equation is $\boxed{x^2 - 18x + 77 = 0}$.

We need to find two numbers that multiply to 77 and add up to -18. These numbers are -7 and -11.

Set each factor to zero to find the roots.

The solutions to the equation are $\boxed{x = 7 \text{ and } x = 11}$.

The roots of the quadratic equation are the two numbers.
Therefore, the two numbers are $\boxed{7 \text{ and } 11}$.