What is the numbers whose sum is 31 and the product is 361

Let the sum of the two numbers x1 and x2 = 31 and their
product  x1x2 = 361. We have to find the numbers x1 and
x2.

So x1 and x2 are the roots of x^2-(x1+x2)x+x1x2 = 0,
or

x^2-31x+361 = 0.

We know
that the roots of the equation ax^2+bx+c = 0 is given by:x1 = {-b+sqrt(b^2-4ac)}/2a
and

x2 =
{-b+sqrt(b^2-4ac)}/2.

Here a = 1, b= -31 and c=
361.

So x1 = {-(-31) + sqrt{(-31)^2 -
4*361)}/2

x1 =
{31+sqrt(-483)}/2

x2 =
{31-sqrt(-483)}/2.

Therefore there are no real numbers
whose sum is 31 and the product is 361. However there is solution in complex numbers..
So , x1 = {31+sqrt(-483)}/2 and x2 = {31-sqrt(-483)}/2 are the
solutions.