Question
(This Project requires that you know some basic facts about complex numbers; so, it is only appropriate if you have studied complex numbers in some mathematics class.) Write a C++ program that solves quadratic equation to find its roots. The roots of a quadratic equation ax^2 + bx + c = 0
(where a is not zero) are given by the formula:
(–b } sqrt(b2 – 4ac)) / 2a
The value of the discriminant (b2 – 4ac) determines the nature of roots. If the value of the discriminant is zero then the equation has a single real root. If the value of the discriminant is positive then the equation has two real roots. If the value of the discriminant is negative, then the equation has two complex roots.
The program takes values of a, b, and c as input and outputs the roots. Be creative in how you output complex roots. Include a loop that allows the user to repeat this calculation for new input values until the user says she or he wants to end the program.
Answer
Program code:
#include<iostream>
#include<cmath>
using namespace std;
void main()
{
int a, b, c;
double d;
char choice;
do
{
cout<<" Quadratic equation form: ax^2 +bx+c = 0"
<<endl;
cout<<" Enter a:";
cin>>a;
cout<<" Enter b:";
cin>>b;
cout<<" Enter c:";
cin>>c;
d = (b*b - 4*a*c);
if(d== 0)
{
cout<<"Root of equation is: "<<-b/a<<endl;
}
else if(d>0)
{
cout<<"Roots of equation are: "
<<(((-1 *b) +sqrt(d))/(2*a));
cout<<" and "<<(((-1 *b) - sqrt(d))/(2*a));
}
else
{
cout<<"Complex Roots."<<endl;
cout<<"Roots of equation: \n"<<
(-1*b)/(2*a)<<" + i"<<sqrt(-1*d)<<endl;
cout<<(-1*b)/(2*a)<<" - i"<<sqrt(-1*d)<<endl;
}
cout<<"If you want to continue then
enter'y' or 'Y':"<<endl;
cin>>choice;
}while(choice =='y' || choice =='Y');
}
Output:
Quadratic equation form: ax^2 +bx+c = 0
Enter a:2
Enter b:4
Enter c:2
Root of equation is: -2
If you want to continue then enter'y' or 'Y': n