Quadratic Equations

 
We are going to create now a Matlab program that calculates the quadratic roots (roots of quadratic equations). The equation must be in the following form:

 ax² + bx + c = 0, where a, b, and c are real coefficients.

 The formula used to calculate the roots is:

 
Naturally, we have to deliver two x-values.

The m-file that we might use to accomplish this task is very simple:

function x = rqe(a,b,c)
x(1) = (-b + sqrt(b^2 - 4 * a * c))/(2*a);
x(2) = (-b - sqrt(b^2 - 4 * a * c))/(2*a);

We enter the coefficients as parameters when we call the function. We assign to variables x(1) and x(2) the calculated values using the formula, and the returning result x is a vector containing x(1) and x(2).

We could use the following Matlab code instead, to return two separate variables:

function [x,y] = rqe2(a,b,c)
x = (-b + sqrt(b^2 - 4 * a * c))/(2*a);
y = (-b - sqrt(b^2 - 4 * a * c))/(2*a);

If we want to compute the roots of the following expression:

2x² + x - 1 = 0

We can call our function (first code) like this:

x = rqe(2,1,-1)

and we get from Matlab:

x =

    0.5000   -1.0000

We can call our second function (second code above) like this:

[m, n] = rqe2(2, 1, -1)

and we get from Matlab:

m =

    0.5000

n =

    -1