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#include <iostream>
#include <cmath>
using namespace std;
void one(){
float a = 0.0; //here we declare the variables and use float because we
float b = 0.0; //are dealing with square roots
float c = 0.0;
float x1 = 0.0;
float x2 = 0.0;
float x3 = 0.0;
float x4 = 0.0;
//this section gets user input and displays message
cout << "Enter the coefficients a , b , c for equation in the form ax^ + bx + c = 0:\n";
cout << "Enter value for a:\n";
cin >> a;
cout << "Enter value for b:\n";
cin >> b;
cout << "Enter value for c:\n";
cin >> c;
//are all the coefficients 0? if so both roots are 0
if(a == 0 && b == 0 && c == 0){
x1 = 0;
x2 = 0;
cout << "The roots are:" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}
//is c the only non-zero number? if so tell the user
if(a == 0 && b == 0 && c != 0){
c = c;
cout << "There are no roots" "\n" << "c = " << c << "\n";
}
//is a zero? if so solve the resulting linear equasion and notify user
if(a == 0 && b != 0 && c !=0){
cout << "The values entered do not make a quadratic expression" "\n"<< "x = " << -c/b << "\n";
}
//if b is zero and c is zero tell user
if(a == 0 && b != 0 && c == 0){
x1 = 0;
x2 = 0;
cout << "The roots are:" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}
//if b and c are equal to zero then ax^=0 and since a cannot be zero without x being
// zero also let user know
if(a != 0 && b == 0 && c == 0){
x1 = 0;
x2 = 0;
cout << "The values entered result in ax^= 0; so both roots are 0" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}
//factor out x from ax^+bx=0 and either x = 0 or ax + b =0
//then solve the linear equation
if(a != 0 && b != 0 && c == 0){
x1 = 0;
x2 = -b/a;
cout << "The roots are:" "\n"
<< "x1 = " << x1 << " , " << "x2 = " << x2 << "\n";
}
//now we get to use the square root function and let the user
//know they have some imaginary numbers to deal with
if(a < 0 && b == 0 && c < 0){
x1 = -b/(2*a);
x4 = (b*b)-(4*a*c);
x4 = -x4;
x2 = sqrt(x4)/(2*a);
x3 = -sqrt(x4)/(2*a);
cout << "The roots are not real numbers:" "\n"
<< "x1 =" << x1 << " + " << x2 << " * i " << "\n"
<< "x2 =" << x1 << " + " << x3 << " * i " << "\n";
}
if(a > 0 && b == 0 && c > 0){
x1 = -b/(2*a);
x4 = (b*b)-(4*a*c);
x4 = -x4;
x2 = sqrt(x4)/(2*a);
x3 = -sqrt(x4)/(2*a);
cout << "The roots are not real numbers:" "\n"
<< "x1 =" << x1 << " + " << x2 << " * i " << "\n"
<< "x2 =" << x1 << " + " << x3 << " * i " << "\n";
}
//now a and c are opposite signs so the answer will be real
if(a > 0 && b == 0 && c < 0){
x1 = (-b + (sqrt(pow(b,2)-(4*a*c))))/(2*a);
x2 = (-b - (sqrt(pow(b,2)-(4*a*c))))/(2*a);
cout << "The roots are:" "\n"
<< "x1 = "<< x1 << " , " << "x2 = "<< x2 << "\n";
}
if(a < 0 && b == 0 && c > 0){
x1 = (-b + (sqrt(pow(b,2)-(4*a*c))))/(2*a);
x2 = (-b - (sqrt(pow(b,2)-(4*a*c))))/(2*a);
cout << "The roots are:" "\n"
<< "x1 = "<< x1 << " , " << "x2 = "<< x2 << "\n";
}
//ok now if we end up not having to take the square root of a neg
// do the math
if(a != 0 && b != 0 && c != 0 && (4*a*c) <= pow(b,2)){
x1 = (-b + (sqrt(pow(b,2)-(4*a*c))))/(2*a);
x2 = (-b - (sqrt(pow(b,2)-(4*a*c))))/(2*a);
cout << "The roots are:" "\n"
<< "x1 = "<< x1 << " , " << "x2 = " << x2 << "\n";
}
//here we have to deal with non x intercepts ie: sqrt(-1)
// alter the formula slightly to give correct output and
// let the user know
if(a != 0 && b != 0 && c != 0 && (4*a*c)> pow(b,2)){
x1 = -b/(2*a);
x4 = (b*b)-(4*a*c);
x4 = -x4;
x2 = sqrt(x4)/(2*a);
x3 = -sqrt(x4)/(2*a);
cout << "The roots are not real numbers" "\n"
<< "x1 =" << x1 << " + " << x2 << " * i " << "\n"
<< "x2 =" << x1 << " + " << x3 << " * i " << "\n";
}
return;
}
//keep output from vanishing before we can read it.
void two(){
char c ;
cout << "Press c and then Enter to continue...." "\n";
cin >> c;
for(;;){
if ( c ){
break;
}
}
cout << "Done" "\n";
}
int main(){
one();
two();
return 0;
}
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