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Solution 1 to 6
Solution 1

Quadratic Equation

This program solves quadratic equations of the form ax2 + bx + c = 0 , It calculates the roots of the equation based on the values of a, b, and c that you provide. Let's go through the code and understand how it works.

Code Breakdown

Algorithm

  1. Start
  2. Input Coefficients: Read the values of a, b, and c.
  3. Check if a is 0:
    • If true, print "Equation is not quadratic" and exit.
  4. Calculate Discriminant d:
    • Compute d using the formula: d = b2 - 4ac
  5. Check Discriminant:
    • If d > 0, calculate two distinct real roots:
      • root1 = (-b + sqrt(d)) / (2 * a)
      • root2 = (-b - sqrt(d)) / (2 * a)
    • If d == 0, calculate one real root:
      • root1 = -b / (2 * a)
    • If d < 0, the roots are imaginary.
  6. Display Results:
    • Print the roots or state that they are imaginary.
  7. End

Code Explanation

//

denotes comments in the code, which are not executed and are not part of the code logic.

Example Flowchart

                            Start
                              |
                              V
                   Input coefficients a, b, c
                              |
                              V
                     Is a equal to 0?
                     /              \
                    /                \
                  Yes                No
                  /                    \
                 /                      \
    Print "Equation is           Calculate Discriminant
       not quadratic"               d = b^2 - 4ac
                |                             |
                |                             |
                V                             V
               End                     Is d greater than 0?
                                         /               \
                                        /                 \
                                      Yes                  No
                                      /  \                  \
                                     /    \                  \
                                    /      \             Is d equal to 0?
                                   /        \             /             \
                                  /          \           Yes            No
                                 /            \          |                \
    +----------------------------+       +------------------------+        \
    |  Calculate roots:           |      |  Calculate root:       |         \
    |  root1 = (-b + sqrt(d)) /   |      |  root1 = -b / (2 * a)  |          \
    |  (2 * a)                    |      +------------------------+           \
    |  root2 = (-b - sqrt(d)) /   |               |                            |
    |  (2 * a)                    |               |                            |
    +----------------------------+                |                            |
                |                                 |                            |
                |                                 |                            |
                V                                 V                            V
           Print roots:                     Print "Roots are            Print "Roots are
         root1 and root2                     real and equal"              imaginary"
                |                                 |                            |
                |                                 |                            |
                V                                 V                            V
               End                               End                          End
FoundationSolution 2