# C++ polynomial operations

#### mathmari

##### Well-known member
MHB Site Helper
Hey!!

I am looking at the following:

a) Create a class QuadraticPolyonym that describes a polynomial of second degree, i.e. of the form $P(x)=ax^2+bx+c, a\neq 0$.The coefficients have to be givenas arguments at the construction ofan instance of the class. Implement a method Discriminant that calculates the discriminant $D=b^2-4ac$.
b) Implement a method Roots that returns a dynamic array (std::vector) with the real roots of $p(x)=0$.
c) Support addition of polynomials with the operator $+$. With elements QuadraticPolyonym p1, p2; thepolynomial QuadraticPolyonym p3 = p1 + p2; should describe a polynomial where the coefficients isteh sum of the corresponding coefficients of the polynomials p1 and p2.
d) Write a program that creates two elements of the class QuadraticPolyonym P(x) and Q(x) reading the coefficinets from the input, adding these to get the polyomial R(x) and printing the roots of R(x)=0\$ at the output.

I have done the following :

Code:
#include <iostream>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>

using namespace std;

//Question(a)
{
private:
double a, b, c;

public:

double Discriminant(double a, double b, double c) { return b*b-4*a*c; }

//Question (b)
double Roots(double a, double b, double c)
{
int x1, x2;
if (Discriminant(a,b,c) > 0) {
x1 = (-b + sqrt(Discriminant(a,b,c))) / (2*a);
x2 = (-b - sqrt(Discriminant(a,b,c))) / (2*a);
cout << "Roots are real and different." << endl;
cout << "x1 = " << x1 << endl;
cout << "x2 = " << x2 << endl;
}

else if (Discriminant(a,b,c) == 0) {
cout << "Roots are real and same." << endl;
x1 = -b/(2*a);
cout << "x1 = x2 =" << x1 << endl;
}

else {
cout << "Roots are complex"  << endl;
}
return 0;
}

//Question (c)
double* OperatorPlus(double x[3], double y[3])
{
double* z=new double[3];
int i;
for( i = 0; i < 3; ++i) {
z[i] = x[i] + y[i];
}
return z;
}

};

//Question (d)
int main()
{
int i;
double coefP[3], coefQ[3],result[3];

cout<<"Enter the coefficients of P:\n";
for(i = 0; i < 3; i++) {
cin>>coefP[i];
}
cout<<"Enter the coefficients of Q:\n";
for(i = 0; i < 3; i++){
cin>>coefQ[i];
}

double* result = R.OperatorPlus(coefP, coefQ); //Question (c)

R.Roots(result[0],result[1], result[2]);

return 0;
}

It doesn't work as it should yet, but am I thinking in a correct way for the program? Or is this completly wrong?

Last edited:

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Hey mathmari !!

It says: The coefficients have to be given as arguments at the construction of an instance of the class.
That means there should be a constructor function named QuadraticPolyonym() with 3 parameters that initializes each of the 3 data members a, b, and c.
It should be used to construct p and q in main() like:
double a, b, c;
cin >> a >> b >> c;
cin >> a >> b >> c;

It says: Implement a method Discriminant.
That means there should be a method named Discriminant() without any parameters that should calculate the discriminant based on the 3 data members a, b, and c.
It should be called in main() like:
cout << "Discriminant P=" << P.Discriminant() << endl;

It says: Implement a method Roots that returns a dynamic array (std::vector).
That means there should be a method std::vector Roots(); without any parameters that returns an std::vector with the roots.

It says: Support addition of polynomials with the operator +.
That means there should be a global function QuadraticPolyonym operator+(const QuadraticPolyonym& p, const QuadraticPolyonym& q) that adds p and q together and returns the result.
It should be called in main() as specified in the problem.

It doesn't say how to read/print the polynomials for (d), so what you have in your main() is okay to read the coefficients.
But we should still construct the polynomials and use the methods we have to process them.

#### mathmari

##### Well-known member
MHB Site Helper
It says: The coefficients have to be given as arguments at the construction of an instance of the class.
That means there should be a constructor function named QuadraticPolyonym() with 3 parameters that initializes each of the 3 data members a, b, and c.
It should be used to construct p and q in main() like:
double a, b, c;
cin >> a >> b >> c;
cin >> a >> b >> c;
What exactly should this constructor function do? I got stuck right now.

It says: Implement a method Discriminant.
That means there should be a method named Discriminant() without any parameters that should calculate the discriminant based on the 3 data members a, b, and c.
It should be called in main() like:
cout << "Discriminant P=" << P.Discriminant() << endl;
Is the part in the class where I defined the discriminant wrong? ;unsure:

It says: Implement a method Roots that returns a dynamic array (std::vector).
That means there should be a method std::vector Roots(); without any parameters that returns an std::vector with the roots.
Should it be :

Code:
std::vector Roots()
{
int x1, x2;
if (Discriminant(a,b,c) > 0 || Discriminant() == 0) {
x1 = (-b + sqrt(Discriminant())) / (2*a);
x2 = (-b - sqrt(Discriminant())) / (2*a);
return {x1,x2}
}

else {
return 0;
}
}

#### mathmari

##### Well-known member
MHB Site Helper
I changed now some things... Now I have:

Code:
#include <iostream>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>

using namespace std;

{
private:
double coef[3];

public:
double Discriminant() {return b*b-4*a*c; }

std::vector Roots()
{
int x1, x2;
if (Discriminant() > 0 || Discriminant() == 0) {
x1 = (-b + sqrt(Discriminant())) / (2*a);
x2 = (-b - sqrt(Discriminant())) / (2*a);
return {x1,x2}
}

else {
return 0;
}
}

double QuadraticPolyonym::getCoef( int k ) const
{
if ( k <= 2 )
return coef[k];
else
return 0.0;
}

{
coef[k] = value;
}

//-- Definition of +
{
double sum;

for ( int i=degree; i >= 0; i-- )
{
sum = P.getCoef( i ) + Q.getCoef( i );
if ( sum != 0.0 )
R.setCoef( i, sum );
}

return R;
}

};

int main()
{
int i;
double coefP[3], coefQ[3];

cout<<"Enter the coefficients of P:\n";
for(i = 0; i < 3; i++) {
cin >> x;
P.setCoef(i,x);
}

cout<<"Enter the coefficients of Q:\n";
for(i = 0; i < 3; i++){
cin >> x;
Q.setCoef(i,x);
}

R=operator+(&P, &Q);

R.Roots();
return 0;
}

I still get some errors. But is this now on the correct way?

#### Country Boy

##### Well-known member
MHB Math Helper
You still don't have a constructor!

It's been a long time since I wrote C++. I prefer Pascal- but they aren't that different.

I think you need something like

{
private
double a, b, c;

QuadraticPolynym(double p, double q, double r)
{ \\constructs the polynomial x^2
a= p; b= q; c= r;
}

#### Klaas van Aarsen

##### MHB Seeker
Staff member
I still get some errors. But is this now on the correct way?
This QuadraticPolyonym exercise and the previous one about Matrix33 are about solving problems with Object Oriented Programming in C++.
• Classes
• Constructors/destructors
• Data members/member functions (aka methods)
• public/protected/private access
QuadraticPolyonym p1, p2;
QuadraticPolyonym p3 = p1 + p2;