\"6.32 Algebra: solve quadratic equations) The two roots of a quadratic equation

Question

"6.32 Algebra: solve quadratic equations) The two roots of a quadratic equation ax2 + bx + x = 0 can be obtained using the following formula: and r2 = 2a 2a Write a function with the following header void solveQuadraticEquation (double a, double b, double c, double& discriminant, double& rl, double& r2) b2 - 4ac is called the discriminant of the quadratic equation. If the discriminant is less than 0, the equation has no roots. In this case, ignore the value in r1 and r2. Write a test program that prompts the user to enter values for a, b, and c and displays the result based on the discriminant. If the discriminant is greater than or equal to 0, display the two roots. If the discriminant is equal to O, display the one root. Otherwise, display the equation has no roots" . See Programming Exercise 3.1 for sample runs.

Explanation / Answer

//solution

#include<iostream>

using namespace std;

void SolveQuadraticEquation(double a, double b, double c, double &discriminant, double& r1, double& r2);

int main()

{

double a, b, c, discriminant, r1, r2;

cout << "Enter value for a : ";

cin >> a;

cout << "Enter value for b : ";

cin >> b;

cout << "Enter value for c : ";

cin >> c;

//call function

SolveQuadraticEquation(a, b, c, discriminant, r1, r2);

cout << "Roots of quadratic equation are r1 = " << r1 << " and r2 = " << r2 << endl;

}

void SolveQuadraticEquation(double a, double b, double c, double &discriminant, double& r1, double& r2)

{

//calclulate discriminant

discriminant = (b*b - 4 * a*c);

if (discriminant < 0)

{

cout << "discriminant is less than zero hence equation has no roots" << endl;

exit(0);

}

discriminant = sqrt(discriminant);

r1 = (-b + discriminant) / 2 * a;

r2 = (-b - discriminant) / 2 * a;

return;

}

-----------------------------------------------------------------------------------------------

//output1

Enter value for a : 1
Enter value for b : 3
Enter value for c : -4
Roots of quadratic equation are r1 = 1 and r2 = -4

//output2

Enter value for a : 1
Enter value for b : -18
Enter value for c : 81
Roots of quadratic equation are r1 = 9 and r2 = 9

//output3

Enter value for a : 3
Enter value for b : -10
Enter value for c : 3
Roots of quadratic equation are r1 = 27 and r2 = 3

//output4

Enter value for a : 1
Enter value for b : 1
Enter value for c : 1
discriminant is less than zero hence equation has no roots

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