Program to find the Roots of Quadratic equation
Given a quadratic equation in the form ax2 + bx + c, find roots of it.
Examples :
Input : a = 1, b = -2, c = 1 Output : Roots are real and same 1 Input : a = 1, b = 7, c = 12 Output : Roots are real and different -3, -4 Input : a = 1, b = 1, c = 1 Output : Roots are complex -0.5 + i1.73205 -0.5 - i1.73205
Below is direct formula for finding roots of quadratic equation.
There are following important cases.
If b*b < 4*a*c, then roots are complex (not real). For example roots of x2 + x + 1, roots are -0.5 + i1.73205 and -0.5 - i1.73205 If b*b == 4*a*c, then roots are real and both roots are same. For example, roots of x2 - 2x + 1 are 1 and 1 If b*b > 4*a*c, then roots are real and different. For example, roots of x2 - 7x - 12 are 3 and 4
Below is the implementation of the above formula.
C
/* C program to find roots of a quadratic equation */ #include <math.h> #include <stdio.h> #include <stdlib.h> // Prints roots of quadratic equation ax*2 + bx + x void findRoots( int a, int b, int c) { // If a is 0, then equation is not quadratic, but // linear if (a == 0) { printf ( "Invalid" ); return ; } int d = b * b - 4 * a * c; double sqrt_val = sqrt ( abs (d)); if (d > 0) { printf ( "Roots are real and different \n" ); printf ( "%f\n%f" , ( double )(-b + sqrt_val) / (2 * a), ( double )(-b - sqrt_val) / (2 * a)); } else if (d == 0) { printf ( "Roots are real and same \n" ); printf ( "%f" , -( double )b / (2 * a)); } else // d < 0 { printf ( "Roots are complex \n" ); printf ( "%f + i%f\n%f - i%f" , -( double )b / (2 * a), sqrt_val, -( double )b / (2 * a), sqrt_val); } } // Driver code int main() { int a = 1, b = -7, c = 12; // Function call findRoots(a, b, c); return 0; } |
C++
/* C++ program to find roots of a quadratic equation */ #include <bits/stdc++.h> using namespace std; // Prints roots of quadratic equation ax*2 + bx + x void findRoots( int a, int b, int c) { // If a is 0, then equation is not quadratic, but // linear if (a == 0) { cout << "Invalid" ; return ; } int d = b * b - 4 * a * c; double sqrt_val = sqrt ( abs (d)); if (d > 0) { cout << "Roots are real and different \n" ; cout << ( double )(-b + sqrt_val) / (2 * a) << "\n" << ( double )(-b - sqrt_val) / (2 * a); } else if (d == 0) { cout << "Roots are real and same \n" ; cout << -( double )b / (2 * a); } else // d < 0 { cout << "Roots are complex \n" ; cout << -( double )b / (2 * a) << " + i" << sqrt_val << "\n" << -( double )b / (2 * a) << " - i" << sqrt_val; } } // Driver code int main() { int a = 1, b = -7, c = 12; // Function call findRoots(a, b, c); return 0; } |
Java
// Java program to find roots // of a quadratic equation import java.io.*; import static java.lang.Math.*; class Quadratic { // Prints roots of quadratic // equation ax * 2 + bx + x static void findRoots( int a, int b, int c) { // If a is 0, then equation is not // quadratic, but linear if (a == 0 ) { System.out.println( "Invalid" ); return ; } int d = b * b - 4 * a * c; double sqrt_val = sqrt(abs(d)); if (d > 0 ) { System.out.println( "Roots are real and different \n" ); System.out.println( ( double )(-b + sqrt_val) / ( 2 * a) + "\n" + ( double )(-b - sqrt_val) / ( 2 * a)); } else if (d == 0 ) { System.out.println( "Roots are real and same \n" ); System.out.println(-( double )b / ( 2 * a) + "\n" + -( double )b / ( 2 * a)); } else // d < 0 { System.out.println( "Roots are complex \n" ); System.out.println(-( double )b / ( 2 * a) + " + i" + sqrt_val + "\n" + -( double )b / ( 2 * a) + " - i" + sqrt_val); } } // Driver code public static void main(String args[]) { int a = 1 , b = - 7 , c = 12 ; // Function call findRoots(a, b, c); } } // This code is contributed by Sumit Kumar. |
Python3
# Python program to find roots # of a quadratic equation import math # Prints roots of quadratic equation # ax*2 + bx + x def findRoots(a, b, c): # If a is 0, then equation is # not quadratic, but linear if a = = 0 : print ( "Invalid" ) return - 1 d = b * b - 4 * a * c sqrt_val = math.sqrt( abs (d)) if d > 0 : print ( "Roots are real and different " ) print (( - b + sqrt_val) / ( 2 * a)) print (( - b - sqrt_val) / ( 2 * a)) elif d = = 0 : print ( "Roots are real and same" ) print ( - b / ( 2 * a)) else : # d<0 print ( "Roots are complex" ) print ( - b / ( 2 * a), " + i" , sqrt_val) print ( - b / ( 2 * a), " - i" , sqrt_val) # Driver Program a = 1 b = - 7 c = 12 # Function call findRoots(a, b, c) # This code is contributed by Sharad Bhardwaj. |
C#
// C# program to find roots // of a quadratic equation using System; class Quadratic { // Prints roots of quadratic // equation ax * 2 + bx + x void findRoots( int a, int b, int c) { // If a is 0, then equation is // not quadratic, but linear if (a == 0) { Console.Write( "Invalid" ); return ; } int d = b * b - 4 * a * c; double sqrt_val = Math.Abs(d); if (d > 0) { Console.Write( "Roots are real and different \n" ); Console.Write( ( double )(-b + sqrt_val) / (2 * a) + "\n" + ( double )(-b - sqrt_val) / (2 * a)); } // d < 0 else { Console.Write( "Roots are complex \n" ); Console.Write(-( double )b / (2 * a) + " + i" + sqrt_val + "\n" + -( double )b / (2 * a) + " - i" + sqrt_val); } } // Driver code public static void Main() { Quadratic obj = new Quadratic(); int a = 1, b = -7, c = 12; // Function call obj.findRoots(a, b, c); } } // This code is contributed by nitin mittal. |
PHP
<?php // PHP program to find roots // of a quadratic equation // Prints roots of quadratic // equation ax*2 + bx + x function findRoots( $a , $b , $c ) { // If a is 0, then equation is // not quadratic, but linear if ( $a == 0) { echo "Invalid" ; return ; } $d = $b * $b - 4 * $a * $c ; $sqrt_val = sqrt( abs ( $d )); if ( $d > 0) { echo "Roots are real and " . "different \n" ; echo (- $b + $sqrt_val ) / (2 * $a ) , "\n" , (- $b - $sqrt_val ) / (2 * $a ); } else if ( $d == 0) { echo "Roots are real and same \n" ; echo - $b / (2 * $a ); } // d < 0 else { echo "Roots are complex \n" ; echo - $b / (2 * $a ) , " + i" , $sqrt_val , "\n" , - $b / (2 * $a ), " - i" , $sqrt_val ; } } // Driver code $a = 1; $b = -7 ; $c = 12; // Function call findRoots( $a , $b , $c ); // This code is contributed // by nitin mittal. ?> |
Javascript
<script> // JavaScript program to find roots // of a quadratic equation // Prints roots of quadratic // equation ax * 2 + bx + x function findRoots(a, b, c) { // If a is 0, then equation is not // quadratic, but linear if (a == 0) { document.write( "Invalid" ); return ; } let d = b * b - 4 * a * c; let sqrt_val = Math.sqrt(Math.abs(d)); if (d > 0) { document.write( "Roots are real and different \n" + "<br/>" ); document.write( (-b + sqrt_val) / (2 * a) + "<br/>" + (-b - sqrt_val) / (2 * a)); } else if (d == 0) { document.write( "Roots are real and same \n" + "<br/>" ); document.write(-b / (2 * a) + "<br/>" + -b / (2 * a)) ; } else // d < 0 { document.write( "Roots are complex \n" ); document.write(-b / (2 * a) + " + i" + sqrt_val + "<br/>" + -b / (2 * a) + " - i" + sqrt_val); } } // Driver Code let a = 1, b = -7, c = 12; // Function call findRoots(a, b, c); </script> |
Output
Roots are real and different 4.000000 3.000000
This article is contributed by Dheeraj Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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