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Python program to find roots of a quadratic equation
Roots of a quadratic equation in Python
Here, in this page we will discuss the program to find the roots of a quadratic equation in python . In this python program, we will learn how to find the roots of a quadratic equation [ax2 + bx + c].
When we try to solve the quadratic equation we find the root of the equation. Mainly roots of the quadratic equation are represented by parabola in 3 different patterns like
- No Real Roots
- One Real Root
- Two Real Roots
When we solve the equation we get 3 conditions mentioned above using this formula:-
X = [-b (+or-) [sqrt(pow(b,2)-4ac)] ] / 2a
Algorithm :
- Calculate Discriminant (D)
- D = b^2 – 4*a*c
- If D>0 : Two real root exists.
- If D=0 : Equal root exists.
- If D<0 : Imaginary root exists.
Code in Python
Run
# Write a program to find roots of a quadratic equation in Python import math def findRoots(a, b, c): 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 = 4 c = 4 # Function call findRoots(a, b, c)
Output :
Roots are real and same
-2.0
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#quadratic equation: x^2 -2x -15
a = 1
b = -2
c = -15
x1 = (-b + (b ** 2 – 4 * a * c) ** 0.5)/ 2 * a
x2 = (-b – (b ** 2 – 4 * a * c) ** 0.5)/2 * a
print(x1)
print(x2)
#more clearly
#quadratic equation: x^2 -2x -15
a = 1
b = -2
c = -15
x1 = (-b + (b ** 2 – 4 * a * c) ** 0.5)/ 2 * a
x2 = (-b – (b ** 2 – 4 * a * c) ** 0.5)/2 * a
print(x1)
print(x2)
Code in Java :
import java.util.Scanner;
public class Quadratic_equation
{
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
System.out.print(“Enter a:”);
int a = sc.nextInt();
System.out.print(“Enter b:”);
int b = sc.nextInt();
System.out.print(“Enter c:”);
int c = sc.nextInt();
int determinant = b*b – 4*a*c;
if(determinant > 0)
{
System.out.println(“Real roots: “);
double root1 = (-b + Math.sqrt(determinant) )/(2*a);
System.out.println(root1);
double root2 = (-b – Math.sqrt(determinant) )/(2*a);
System.out.println(root2);
}
else if(determinant < 0)
{
System.out.println("Imaginary roots: ");
double root1 = -b/(2*a);
double rootImg1 = Math.abs(Math.sqrt(determinant));
System.out.println(root1 +"+i"+rootImg1);
System.out.println(root1 +"-i"+rootImg1); // Imaginary root2
}
else
{
System.out.println("Equal roots: ");
System.out.println(-b/2*a);
System.out.println(-b/2*a);
}
}
}