Given three integers a, b and c such that a + b + c = 0. The task is to find the roots of a quadratic equation ax2 + bx + c = 0.
Examples:
Input: a = 1, b = 2, c = -3
Output: 1, -3
Input: a = -5, b = 3, c = 2
Output: 1, -2.5
Approach: When a + b + c = 0 then the roots of the equation ax2 + bx + c = 0 are always 1 and c / a.
For example,
Take a = 3, b = 2 and c = -5 such that a + b + c = 0
Now, the equation will be 3x2 + 2x – 5 = 0
Solving for x,
3x2 + 5x – 3x – 5 = 0
x * (3x + 5) -1 * (3x + 5) = 0
(x – 1) * (3x + 5) = 0
x = 1, x = (-5 / 3) = (c / a)
Below is the implementation of the above approach:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
// Function to print the roots of the // quadratic equation when a + b + c = 0 void printRoots( long a, long b, long c)
{ cout << 1 << ", " << c / (a * 1.0);
} // Driver code int main()
{ long a = 2;
long b = 3;
long c = -5;
printRoots(a, b, c);
return 0;
} |
// Java implementation of the approach class GFG
{ // Function to print the roots of the
// quadratic equation when a + b + c = 0
static void printRoots( long a, long b, long c)
{
System.out.println( 1 + ", " + c / (a * 1.0 ));
}
// Driver Code
public static void main (String[] args)
{
long a = 2 ;
long b = 3 ;
long c = - 5 ;
printRoots(a, b, c);
}
} // This code is contributed by // sanjeev2552 |
# Python3 implementation of the approach # Function to print the roots of the # quadratic equation when a + b + c = 0 def printRoots(a, b, c):
print ( 1 , "," , c / (a * 1.0 ))
# Driver code a = 2
b = 3
c = - 5
printRoots(a, b, c) # This code is contributed by Mohit Kumar |
// C# implementation of the approach using System;
class GFG
{ // Function to print the roots of the // quadratic equation when a + b + c = 0 static void printRoots( long a, long b, long c)
{ Console.WriteLine( "1, " + c / (a * 1.0));
} // Driver code public static void Main()
{ long a = 2;
long b = 3;
long c = -5;
printRoots(a, b, c);
} } // This code is contributed by Nidhi |
<?php // PHP implementation of the approach // Function to print the roots of the // quadratic equation when a + b + c = 0 function printRoots( $a , $b , $c )
{ echo "1" ;
echo ", " ;
echo $c / ( $a * 1.0);
} // Driver code $a = 2;
$b = 3;
$c = -5;
printRoots( $a , $b , $c );
// This code is contributed by Naman_Garg. ?> |
<script> // Javascript implementation of the approach // Function to print the roots of the // quadratic equation when a + b + c = 0 function printRoots(a, b, c)
{ document.write(1 + ", " + c / (a * 1.0));
} // Driver code var a = 2;
var b = 3;
var c = -5;
printRoots(a, b, c); // This code is contributed by noob2000. </script> |
1, -2.5
Time Complexity: O(1), there is only basic arithmetic that happens in constant time.
Auxiliary Space: O(1), no extra space is taken.