Polynomial evaluation and roots in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What MATLAB function is used to evaluate a polynomial at specific points?

The polyval function evaluates a polynomial at given points. You provide the polynomial coefficients and the points where you want to evaluate it.

beginner

How do you find the roots of a polynomial in MATLAB?

Use the roots function with the polynomial coefficients as input. It returns the values where the polynomial equals zero.

beginner

Given polynomial coefficients p = [1 -3 2], what polynomial does this represent?

It represents the polynomial x² - 3x + 2. The vector lists coefficients from highest degree to constant term.

intermediate

What is the output of roots([1 -3 2]) in MATLAB?

The output is [2; 1], which are the roots of the polynomial x² - 3x + 2.

beginner

How can you evaluate the polynomial x² - 3x + 2 at x = 5 in MATLAB?

Use polyval([1 -3 2], 5). This calculates 5² - 3*5 + 2 = 25 - 15 + 2 = 12.

Which MATLAB function returns the roots of a polynomial given its coefficients?

A polyfit

B polyval

C rootsolve

D roots

The roots function finds the zeros of the polynomial.

What does the vector [2 -4 1] represent in MATLAB polynomial terms?

A 2x² - 4x + 1

B 2 + -4x + x²

C x² - 4x + 2

D 1x² - 4x + 2

Coefficients are listed from highest degree to constant term.

What will polyval([1 0 -1], 1) return?

A 0

B 1

C -1

D 2

Evaluates x² - 1 at x=1: 1² - 1 = 0.

If a polynomial has coefficients [1 -2 1], what are its roots?

A [-1; -1]

B [1; 1]

C [0; 1]

D [2; -1]

The polynomial x² - 2x + 1 factors as (x-1)², root at 1.

Which MATLAB function would you use to fit a polynomial to data points?

A roots

B polyval

C polyfit

D polyroot

polyfit fits a polynomial to data, not for evaluation or roots.

Explain how to represent a polynomial in MATLAB and how to evaluate it at a given point.

Think about how you write the polynomial as a list of numbers and then use a function to find its value.

Describe the process to find the roots of a polynomial using MATLAB and what the roots represent.

Roots are where the polynomial equals zero.