A quadratic equation is a polynomial equation, having highest degree of two. The equation is represented in the form of ax²+bx+c where a can’t be 0, c is constant, a and b are coefficients. There can be two answers of x which is termed as roots.

This Quadratic formula is applied only when b2– 4ac >= 0.
such that,
If b²– 4ac > 0 , means the eqn. has more than one real roots
if b²– 4ac = 0 , represent equal or single root
if b²– 4ac <0, represents imaginary root
Lastly, if a is 0, then the equation would not be considered as a quadratic equation.

A quadratic equation is an equation having a degree of 2.  There are 4 possibilities, these are real roots, equal roots, imaginary roots and not a quadratic equation.

Steps to calculate quadratic equation

• Read a, b, c values
• if a == 0, then it’s not a quadratic equation
• else,
  calculate result = b² – 4ac
  • if result > 0 then
    compute the real roots using the formula
    print root1,root2 values
  • Else if result = 0 then
    compute the equal roots using the formula
    print root1,root2 values
  • Else if result < 0 then
    roots are imaginary
    print no solution

C Program for Quadratic Equation

Program:

#include<conio.h>
#include<stdio.h>
#include<math.h>
void main (){
  float a, b, c, result;
  printf (" ax^2 + bx + c, \n enter the values of a, b and c : = ");
  scanf ("%f %f %f", &a, &b, &c);

  result = (b * b) - (4 * a * c);
  if (a == 0)
    printf ("The equation is not a quadratic equation");
  else if (result > 0)
    {
      result = sqrt (result);
      printf ("Real roots are, %f,%f \n", (-b - result) / (2 * a),
        (-b + result) / (2 * a));
    }
  else if (result == 0)
    {
      result = sqrt (result);
      printf ("equal root, %f,%f \n", (-b) / (2 * a), (-b) / (2 * a));
    }
  else
    {
      printf ("Root are imaginary ;\n No Solution");
    }

  getch ();
}

Output:

Imaginary Roots or No solution

ax^2 + bx + c, 
 enter the values of a, b and c : = 11 5 5
Root are imaginary ;
 No Solution

Real roots:

 ax^2 + bx + c, 
 enter the values of a, b and c : = 5 5 1
Real roots are, -0.723607,-0.276393 

Equal roots:

 ax^2 + bx + c, 
 enter the values of a, b and c : = 5 10 5
equal root, -1.000000,-1.000000 

Not Quadratic

 ax^2 + bx + c, 
 enter the values of a, b and c : = 0 5 5 
The equation is not a quadratic equation