Question 6: 4 marks Write a MATLAB function which will calculate the roots of a

Question

Question 6: 4 marks Write a MATLAB function which will calculate the roots of a quadratic equation. Notes: MATLAB has a built in function called roots to calculate the roots of a quadratic equation. However, you are required to create a MATLAB function which performance that calculation Make sure to state all the assumptions, write all the equations and present flow of your function in your report Pick an example of a quadratic functionland compare the results of the function you created with the results of the MATLAB built in function.

Explanation / Answer

Background

We need to have the equation in the following form:

ax2 + bx + c = 0

where a, b, and c are real coefficients.

The formula used to calculate the roots is:

Let us consider the following quadratic equation which needs to be solved.

2x2 + 4x - 3 = 0, we identify the coefficients a, b and c as 2, 4 and -3 respectively. These coefficients should be given to the program.

Following MATLAB program calculates the roots of a quadratic equation.

In the command window of MATLAB, Open a new m-file and write the following codes.

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);

x = rqe(2, 4, -3)

then MATLAB returns

x =     0.5811 -2.5812

We assign to variables x1 and x2 the calculated values using the formula, and the returning result x is a vector containing x 1 and x 2.The returning result is a vecor which gives the values of x1, x2.

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