Roots of a quadratic equation in C

18CPL17/27

Program 2:-

Develop a program to compute the roots of a quadratic equation by accepting the coefficients. Print appropriate messages.

Quadratic Equation?

ax2 + bx + c = 0
a=0 not a quadratic equation.
Roots of quadratic equation x=(​​-b+ or -sqrt(b*b-4*a*c))/2*a
(b*b − 4ac) is Determinant(D).
If D=0 (root are equal)
If D>0(roots are distinct and real)
If D<0(roots are imaginary) and have two-part
real=-b/(2*a);
imaginary=sqrt(fabs(determinant))/(2*a);

ALGORITHM 

 Purpose: To find roots of a given quadratic equation.

 Input: Coefficients of the quadratic equation a, b, c

 Output: Root1 and Root2 

 START 

 STEP 1: [Input the values of a, b, c] 
 read a, b, c 

 STEP 2: [Calculate the determinant] 
 determinant = b*b-4*a*c 

 STEP 3: [Check for validity] 
 If a is equal to 0 and b is equal to 0 
 print “Invalid Inputs” 

 STEP 4: [Check for different roots] 
 If a is equal to 0 
 print “Linear equation” 
 Root1=-c/b 
 Print “Root1” 

 STEP 5: [Check for real and equal roots] 
 If determinant is equal to 0 
 print “Roots are real and equal” 
 Root1= -b/(2*a) 
 Root2 = -b/(2*a) 
 Print “Root1 & Root2” 

 STEP 6: [Check for real and distinct roots] 
 If determinant is greater than 0 
 Then print “Roots are real and distinct” 
 Root1= (-b+ (sqrt (fabs (determinant))))/(2*a) 

 Root2= (-b-(sqrt (fabs (determinant))))/(2*a)
Print “root1 and root2” 
 End if 

 STEP 7: [Check for imaginary roots] 
 print “Roots are imaginary” 
 Real=-b/ (2*a) 
 Imaginary=sqrt (fabs (determinant))/ (2*a) 
 print “Root1 and R oot2” 

 STEP 8: [Finished] 

 STOP 

FlowChart:-

C Code:-

/****************************************************************************** http://getwayssolution.com/ *******************************************************************************/ #include <stdio.h> #include <math.h> int main() { float a,b,c,real,imaginary,determinant; printf("Enter The Coefficient a,b,c of Quadratic Equation"); scanf("%f %f %f",&a,&b,&c); if(a==0) { printf("Invalid Quadratic Equation\n"); } else { determinant=b*b-4*a*c; if(determinant==0) { printf("Roots are real and equal = %f",-b/2*a*c); } else if(determinant>0) { printf("Roots real and distinct root1=%f \t root2=%f\n",-b+sqrt(abs(determinant))/2*a*c,-b-sqrt(abs(determinant))/2*a*c); } else { real=-b/2*a*c; imaginary=sqrt(abs(determinant))/2*a*c; printf("Roots imaginary\n real part=%f \n imaginary part=(%f)i\n",real,imaginary); } } return 0; }

 ****************************************************************************** 

 Output 1: 

 Enter the Co-efficient of Quadratic Equation 

 000 

 Invalid Coefficients 

Output 2: 

 Enter the Co-efficient of Quadratic Equation 

 0 21 Root1=-0.5

 Output 3: 

 Enter the Co-efficient of Quadratic Equation 

 121 

 Roots are Real and Equal 

 Root1=-1.0000 

 Root2=-1.0000

Output 4: 

 Enter the Co-efficient of Quadratic Equation 

 189 

 Roots are Real and Distinct 

 Root1=-1.354 

 Root2=-6.646 

Output 5: 

 Enter the Co-efficient of Quadratic Equation 

 123 

 ROOTS ARE IMAGINARY 

 ROOT1=-1.000+i1.414 

 ROOT2=-1.000-i1.414 

 ******************************************************************************