I can't get an answer for the quadratic; it just skips right to the "Try again?"
int main()
{
double a, b, c;
double Pos;
double Neg;
char tryagain;
cout << "Enter the coefficient of the quadratic term" << endl;
cin >> a;
cout << "Enter the coefficient of the linear term" << endl;
cin >> b;
cout << "Enter the constant term" << endl;
cin >> c;
do{
if(b*b > 4.0*a*c){
Pos =(-b+sqrt((b*b)-(4*a*c)))/(2*a);
cout << "The positive root is " << setprecision(5) << Pos << endl;
Don't use cin >>foo. It leaves characters in the input buffer and it all gets messy later on. Use std::getline() instead. There are articles some member of the forum have written about various ways of getting input.
I recommend adding a few output statements right after input to ensure the data is correct. For example, right after inputting a, b, and c. That way, you can confirm that the inputs are correct before proceeding further.