Write a spreadsheet that solves the quadratic equation. Recall that a quadratic equation is a polynomial of the form:

ax

^{2}+ bx + c = 0

where a, b, and c are real constants. The "roots" of a quadratic equation are real or complex values of x that satisfy the equation (when you plug in x with the selected values of a, b, and c, the equation evaluates to zero).

The calculations and decision making should all be performed
in VB. The user should enter the coefficients a, b, &
c and then select a **Solve** button. You
should then read the values of a, b, & c and then display the
results. For example, your spreadsheet may look something
like this:

When **a** is not equal to zero, the roots are
given by

The expression under the square root sign (b^{2}
- 4ac) is the discriminant. It would be helpful to write code for the
discriminant that would be used in your if statement.

If the discriminant is positive, then **two real
roots** exist.

If the discriminant is zero, then the two roots are real and
equal. In this case we say that the polynomial has **one
real root**.

If the discriminant is negative, then the roots are **complex**.

When both a = 0 and b = 0, we consider the case **extremely
degenerate** and leave it at that (no roots).

When a = 0 and b is not = 0, we consider the case **degenerate**.
In this case the equation reduces to

bx + c = 0

and it has one root given by x = -c / b.

For each set of values for a, b, and c your spreadsheet should print the computed root(s) along with one of the following messages:

extremely degenerate

degenerate

one real root

two real roots

two complex roots

When you are computing the complex roots, you need to compute two numbers: the real part and the complex part. Compute as (this is psuedo-code, not real VB code):

In other words, take the absolute value of the discriminant before taking the square root.

Then you print the two roots using something like:

Range("B12") = FormatNumber(real,3) & "+ i*" & FormatNumber(complex, 3)

Range("B13") = FormatNumber(real,3) & "- i*" & FormatNumber(complex, 3)

For example, if the values 1, 2, and 3 are specified for a, b, and c respectively, then

two complex roots:

root1 = -1.000 + i*1.414

root2 = -1.000 - i*1.414

should be displayed somewhere in the cells of your spreadsheet.

A good way to set up the code is as follows (this is "psuedo-code"):

Get values for A,B,C from the appropriate cells in the spreadsheet

Compute the discriminant

- if A is equal to zero and B is equal to zero

set result cell to "extremely degenerate"

else if A is equal to zero and B is not equal to zero

set result cell to "degenerate"

set root cells to display appropriate root

else if discrimanant is less than zero

set result cell to "two complex roots"

set root cells to display roots

etc.

- etc.
- End If

Hint: VBA will read your code from top to bottom. Keep this in mind when doing the if statement: order matters.

1. Be sure to save the changes to your spreadsheet.

2. Upload your spreadsheet via Learning Suite.