The program calculates whether a quadratic equation has real roots or imaginary roots.
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
- if result > 0 then
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:
Equal roots:
Not Quadratic