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Published on 10 Mar 2020

Program to find all the roots of a quadratic equation is discussed here.

The general form of a quadratic equation is **(ax^2 + bx + c = 0). **The highest degree in a quadratic equation is 2. Hence, a quadratic equation will have two roots.

The formula to find the roots of a quadratic equation is given as follows

** x = [-b +/- sqrt(-b^2 - 4ac)]/2a**

The discriminant of the quadratic equation is

k = (**b^2 - 4ac).**

Depending upon the nature of the discriminant, the roots can be found in different ways.

- If the
**discriminant is positive**, then there are two distinct real roots. - If the
**discriminant is zero**, then the two roots are equal. - If the
**discriminant is negative**, then there are two distinct complex roots.

**Case 1:** If the discriminant is positive,

**r1 = (-b +?k)/ 2a** and **r2 =(b +?k)/ 2a** are the two roots.

**Case 2:** If the discriminant is zero,

**r1 = r2 = (-b / 2a)**are the two roots.

**Case 3:** If the discriminant is negative,

**r1 = (-b +i ?k)/ 2a** and **r2 =(b + i?k)/ 2a** are the two roots.

```
For example, consider the following equation
2x^2 8x + 3 = 0.
a = 2, b = -8, c = 3
Discriminant value, k =b^2 - 4ac
= 8^2 - 4*(-8)*3
= 40
The discriminant value is positive. Hence, the roots are real and distinct.
r1 = (-b +?k)/ 2a
= (8 +?40) /2*2
= 2.3875
r2 =(b +?k)/ 2a
=(-8 +?40) /2*2
= -0.3875
r1 = 2.3875andr2 = -0.3875 are the two roots.
```

1. Input the value of a, b, c.

2. Calculate k = b*b - 4*a*c

3. If (d < 0)

Display "Roots are Imaginary, calculater1 = (-b +i ?k)/ 2a and r2 =(b + i?k)/ 2a.

else if (d = 0)

Display "Roots are Equal" and calculate r1 = r2 = (-b / 2*a)

else

Display "Roots are real and calculate r1 = -b + ?d / 2*a andr2 = -b - ?d / 2*a

4. Print r1 and r2.

5. End the algorithm.

C

C++

Java

Python 3

Output

Input-
Enter coefficients a, b and c: 1 2 3
Output-
root1 =-1+1.41421 and root2 =-1+1.41421

**Time complexity:** O(1)

*Recommended Programs*

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