The roots of the quadratic equation ax2 bx c 0 a notequal

The roots of the quadratic equation ax^2 + bx + c = 0, a notequalto 0 are given by the following formula: -b plusminus Squareroot b^2 - 4ac/2a In this formula, the term b^2 - 4ac is called the discriminant. If b^2 - 4ac = 0, the equation has a single (repeated) root. If b^2 - 4ac > 0, the equation has two real roots. If b^2 - 4ac

Solution

PROGRAM CODE:

/*

* quadratic.cpp

*

* Created on: 15-Nov-2016

* Author: Kaju

*/

#include <iostream>
#include <math.h>
#include <iomanip>
#include <string>
using namespace std;

class quadraticEq

{

public:

int a,b,c;

float discriminant;

float realRoots[2];

string complexRoots[2];

bool isComplex;

quadraticEq()

{

a = 0;

b = 0;

c = 0;

discriminant = 0;

isComplex = false;

}

quadraticEq(int in_a, int in_b, int in_c)

{

a = in_a;

b = in_b;

c = in_c;

discriminant = calcDiscriminant();

}

double calcDiscriminant()

{

//cout<<sqrt(pow(b,2) - (4*a*c));
float val = pow(b,2) - (4*a*c);
       //cout<<val;
return val;

}

int numberOfroots()

{

if(discriminant == 0)

return 1;

else

return 2;

}

void calcRoots()

{

if(numberOfroots() == 1)

{

// realRoots = new double[1];
realRoots[0] = (-1*b)/(2*a);

}

else

{

if(discriminant < 0)

{

// complexRoots = new string[2];
int discri = discriminant * -1;

float val1 = (-1.0*b)/(2*a) ;
//cout<<\"val1: \"<<val1;
float val2 = sqrt(discri)/(2*a);

complexRoots[0] = to_string(val1) + \" \" ;
if(val2>0)
                   complexRoots[0] = complexRoots[0] + \"+ \";
               complexRoots[0] = complexRoots[0] + to_string(val2) + \"i\";

complexRoots[1] = to_string(val1) + \" \" ;
               val2 = -1*val2;
               if(val2>0)
                   complexRoots[1] = complexRoots[1] + \"+ \";
complexRoots[1] = complexRoots[1] + to_string(val2) + \"i\";

isComplex = true;

}

else

{

// realRoots = new double[2];
float squareroot = sqrt(discriminant);
float root1 = ((-1*b) + squareroot) /(2*a);
realRoots[0] = root1;
float root2 = ((-1*b) - squareroot)/(2*a);
realRoots[1] = root2;

}

}

}

quadraticEq operator +(const quadraticEq &eq)

{

quadraticEq equation;

equation.a = this->a + eq.a;

equation.b = this->b + eq.b;

equation.c = this->c + eq.c;

equation.discriminant = calcDiscriminant();

return equation;

}

quadraticEq operator -(const quadraticEq &eq)

{

quadraticEq equation;

equation.a = this->a - eq.a;

equation.b = this->b - eq.b;

equation.c = this->c - eq.c;

equation.discriminant = calcDiscriminant();

return equation;

}

bool operator ==(const quadraticEq &eq)

{

if(this->a == eq.a && this->b == eq.b && this->c == eq.c)

return true;

else

return false;

}

bool operator !=(const quadraticEq &eq)

{

if(this->a != eq.a || this->b != eq.b || this->c != eq.c)

return true;

else

return false;

}

friend ostream &operator<<( ostream &output, const quadraticEq &eq )

{
   output<<\"\ The equation is\\t\";
output << eq.a<< \"x^2 + \" << eq.b<<\"x + \" << eq.c <<\" = 0\"<<endl;

if(!eq.isComplex)

{

int length = (sizeof(eq.realRoots)/sizeof(*eq.realRoots));
//output<<fixed;
       output<<\"The roots are \\t\";
for(int i=0; i<length; i++)

{
          
output<<\"Root\"<<i+1<<\": \" <<eq.realRoots[i] << \"\\t\";

}

}

else

{

int length = (sizeof(eq.complexRoots)/sizeof(*eq.complexRoots));

for(int i=0; i<length; i++)

   {
  
   output<<\"Root : \" <<eq.complexRoots[i] << \"\\t\";
  
   }

}

return output;

}

friend istream &operator>>( istream &input, quadraticEq &eq )

{

input >> eq.a >>eq.b >>eq.c;

eq.discriminant = eq.calcDiscriminant();

return input;

}

};

int main()

{

quadraticEq eq1, eq2(1,1,1), eq3(1,5,6);

cout<<\"Enter the coefficients for equation1: \";

cin>>eq1;

eq1.calcRoots();

cout<<eq1;

cout<<\"\ \ Equation 2: \"<<endl;

eq2.calcRoots();

cout<<eq2;

cout<<\"\ \ Adding equation 1 and equation 3\"<<endl;

quadraticEq eq4 = eq1 + eq3;

eq4.calcRoots();

cout<<eq4;

cout<<\"\ \ Subtracting equation 1 and equation 3\"<<endl;

quadraticEq eq5 = eq1 - eq3;

eq5.calcRoots();

cout<<eq5;
}

OUTPUT:

Enter the coefficients for equation1: 5 7 9
The equation is   5x^2 + 7x + 9 = 0
Root : -0.700000 + 1.144552i   Root : -0.700000 -1.144552i  

Equation 2:

The equation is   1x^2 + 1x + 1 = 0
Root : -0.500000 + 0.866025i   Root : -0.500000 -0.866025i  

Adding equation 1 and equation 3

The equation is   6x^2 + 12x + 15 = 0
Root : -1.000000 + 0.953794i   Root : -1.000000 -0.953794i  

Subtracting equation 1 and equation 3

The equation is   4x^2 + 2x + 3 = 0
Root : -0.250000 + 1.430690i   Root : -0.250000 -1.430690i