Algorithm for Roots of a Quadratic The roots of a quadratic equation ax^2 + bx + c = 0 can be determined with the quadratic formula, x1 x2 = -b ± √|b^2 - 4ac|/2a (E2.1.1) an algorithm that does the following: Step 1: Prompts the user for the coefﬁcients, a, b, and c. Step 2: Implements the

Question

Algorithm for Roots of a Quadratic

The roots of a quadratic equation

[latex]ax^2 + bx + c = 0[/latex]

can be determined with the quadratic formula,

[latex]\begin{matrix}x_{1} \ x_{2} \end{matrix}= \frac{- b \pm \sqrt{|b^2 - 4ac|} }{2a}[/latex] (E2.1.1)

Develop an algorithm that does the following:

Step 1: Prompts the user for the coefficients, a, b, and c.
Step 2: Implements the quadratic formula, guarding against all eventualities (for example, avoiding division by zero and allowing for complex roots).
Step 3: Displays the solution, that is, the values for x.
Step 4: Allows the user the option to return to step 1 and repeat the process.

Accepted Answer

We will use a top-down approach to develop our algorithm. That is, we will successively refi ne the algorithm rather than trying to work out all the details the first time around.

To do this, let us assume for the present that the quadratic formula is foolproof regardless of the values of the coefficients (obviously not true, but good enough for now). A structured algorithm to implement the scheme is

Question 2.1: Algorithm for Roots of a Quadratic The roots of a quadratic ...

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