Polynomial evaluation and roots in MATLAB - Mini Project: Build & Apply

Polynomial evaluation and roots

📖 Scenario: You are working with polynomials in MATLAB. Polynomials are expressions like 2x2 + 3x + 1. You want to evaluate the polynomial for different values of x and find where the polynomial equals zero (its roots).

🎯 Goal: Build a MATLAB script that defines a polynomial, evaluates it at given points, and finds its roots.

📋 What You'll Learn

Create a vector called p with the polynomial coefficients in descending powers.

Create a vector called x_values with points to evaluate the polynomial.

Use polyval to evaluate the polynomial at x_values and store results in y_values.

Use roots to find the roots of the polynomial and store them in p_roots.

Display the evaluated values and roots using disp.

💡 Why This Matters

🌍 Real World

Polynomials are used in physics, engineering, and computer graphics to model curves and solve equations.

💼 Career

Understanding polynomial evaluation and root finding is important for data analysis, control systems, and algorithm development.

1

Create the polynomial coefficients vector

Create a vector called p with the coefficients [2 3 1] representing the polynomial 2x^2 + 3x + 1.

MATLAB

% Create the polynomial coefficients vector p
% Your code here

Need a hint?

Use square brackets to create a vector with the coefficients in order from highest power to lowest.

2

Create the vector of x values to evaluate

Create a vector called x_values with the values [-1 0 1 2] where you want to evaluate the polynomial.

MATLAB

p = [2 3 1];
% Create the vector x_values with [-1 0 1 2]
% Your code here

Need a hint?

Use square brackets to list the x values exactly as given.

3

Evaluate the polynomial at the given x values

Use polyval with the vector p and x_values to calculate the polynomial values. Store the result in a vector called y_values.

MATLAB

p = [2 3 1];
x_values = [-1 0 1 2];
% Evaluate the polynomial at x_values and store in y_values
% Your code here

Need a hint?

Use polyval(p, x_values) to evaluate the polynomial at all points in x_values.

4

Find and display the roots and evaluated values

Use roots with the vector p to find the roots of the polynomial and store them in p_roots. Then display y_values and p_roots using disp.

MATLAB

p = [2 3 1];
x_values = [-1 0 1 2];
y_values = polyval(p, x_values);
% Find roots and display y_values and p_roots
% Your code here

Need a hint?

Use p_roots = roots(p); to find roots and disp to show results.