C++ :: Quadratic Formula Loss Of Significance And Simplification

write codes that could solve a quadratic formula, and my codes are like this:

#include <bjarne/std_lib_facilities.h>
int main()
{
cout << "Enter the coefficients of a quadratic polynomial a*x**2 + b*x +c:
";
cout << " a? ";
double a;
cin >> a;
cout << " b? ";

[code]....

Which runs perfectly, but I have 2 questions:

1. How to simplify these code? On the assignment sheet the professor wrote about using void solve_linear(double b, double c); and void solve_ quadratic (double a, double b, double c);which I currently dont understand how these works. He asked us to write a well-encapsulated (as short as possible) program.

2. These are for extra points: the precision problem of floating numbers: professor asked us to find a way to get the precise answer of it, like this: Enter the coefficients of a quadratic polynomial a*x**2 + b*x +c:
a? 1
b? -20000
c? 1.5e-9
Trying to solve the quadratic equation 1*x*x + -20000*x + 1.5e-09 == 0
Using classical formula: Two roots, x = 20000 and x = 0
Using stable formula: Two roots, x = 20000 and x = 7.5e-14

My guess is that
A. Using code like if(x1*x2=a/c) to check if numbers were approximated.
B. Somehow determine the larger one in x1 and x2.
C. Somehow use that larger one to do something