Project Task #3: Write a MATLAB function that determines the probability that a random quadratic polynomial q(x)=ax^2+bx+c will have real roots. Do this calculation WITHOUT using a FOR loop!
COMMENT: Assume that the coefficients a, b, and c are generated from the randn() function.
Normally, your procedure would be:
initialize p to 0. for i = 1 : m generate a, b, c, using randn(); determine if q(x) has real roots. if real roots, increase p by 1. end p = p / m
However, you need to do this calculation without using a FOR loop. Instead, you should use vector operations.
INSTRUCTIONS:
Write a function header with input M and output P. function p = p3 ( m ) a = ( a vector of M values produced by randn ) b = (similar) c = (similar) d = a quantity whose value determines whether there are real roots i = logical vector that checks which entries of d have the "right" value p = how many entries in i correspond to real roots p = p / m return end
CHECK: If your code is correct, then as M increases, you should expect the value of the probability p to be about 0.64
SUBMIT: Your function file should be called "p3.m", and should begin with:
% p3.m % YOUR NAME % This script (describe what it does)