Here given a quadratic equation the task is to solve the equation or find out the roots of the equation. The standard form of **a quadratic equation** is –

```
ax2 + bx + c
where,
a, b, and c are coefficient and real numbers and also a ≠ 0.
If a is equal to 0 that equation is not valid quadratic equation.
```

**Examples Of Quadratic Equation: **

```
Input :a = 1, b = 2, c = 1
Output :
Roots are real and same
-1.0
Input :a = 2, b = 2, c = 1
Output :
Roots are complex
-0.5 + i 2.0
-0.5 - i 2.0
Input :a = 1, b = 10, c = -24
Output :
Roots are real and different
2.0
-12.0
```

**Method 1:** **Using the direct formula **

**So here we describes different cases of Quadratic Equation:**

```
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 program illustrate the quadratic equation in Python:**

# Python program to find roots of quadratic equation import math # function for finding roots def equationroots( a, b, c): # calculating discriminant using formula dis = b * b - 4 * a * c sqrt_val = math.sqrt(abs(dis)) # checking condition for discriminant if dis > 0: print(" real and different roots ") print((-b + sqrt_val)/(2 * a)) print((-b - sqrt_val)/(2 * a)) elif dis == 0: print(" real and same roots") print(-b / (2 * a)) # when discriminant is less than 0 else: print("Complex Roots") print(- b / (2 * a), " + i", sqrt_val) print(- b / (2 * a), " - i", sqrt_val) # Driver Program a = 1 b = 10 c = -24 # If a is 0, then incorrect equation if a == 0: print("Input correct quadratic equation") else: equationroots(a, b, c)

**Output:**

```
real and different roots
2.0
-12.0
```

**Method-2:** **Using Complex Math Module**

# import complex math module import cmath a = 1 b = 4 c = 2 # calculating the discriminant dis = (b**2) - (4 * a*c) # find two results ans1 = (-b-cmath.sqrt(dis))/(2 * a) ans2 = (-b + cmath.sqrt(dis))/(2 * a) # printing the results print('The roots are') print(ans1) print(ans2)

**Output:**

```
The roots are
(-3.414213562373095+0j)
(-0.5857864376269049+0j)
```

Please write comments or WhatsApp if you find anything incorrect, or you want to share more information about this topic discussed above.