Polynomial operations with np.poly in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of polynomial addition using np.polyadd

What is the output of this code that adds two polynomials using np.polyadd?

NumPy

import numpy as np
p1 = np.array([1, -3, 2])  # x^2 - 3x + 2
p2 = np.array([0, 4, -1])  # 4x - 1
result = np.polyadd(p1, p2)
print(result)

A [ 1 -3 6 1]

B [ 1 1 1]

C ]1 1 1 [

D 1 1 1]

💡 Hint

Remember that np.polyadd adds coefficients of the same degree terms.

The polynomials are p1 = x^2 - 3x + 2 and p2 = 4x - 1. Adding them gives x^2 + ( -3 + 4 )x + (2 - 1) = x^2 + x + 1, so coefficients are [1, 1, 1].

❓ data_output

intermediate

Degree of polynomial from roots using np.poly

Given roots [-1, 0, 2], what is the degree and coefficients of the polynomial generated by np.poly?

NumPy

import numpy as np
roots = [-1, 0, 2]
coeffs = np.poly(roots)
degree = len(coeffs) - 1
print(degree)
print(coeffs)

A

3
[ 1. -1.  2.  0.]

B

].0  .2- .1- .1 [
3

C

3
[ 1. -1. -2.  0.]

D

].0  .2  .1- .1 [
3

💡 Hint

np.poly returns coefficients of polynomial with given roots, highest degree first.

The polynomial with roots -1, 0, 2 is (x+1)(x)(x-2) = x^3 - x^2 - 2x. Coefficients are [1, -1, -2, 0]. Degree is 3.

❓ visualization

advanced

Plot polynomial and its derivative

Which option correctly plots the polynomial p(x) = 2x^3 - 3x^2 + x - 5 and its derivative using np.polyder?

NumPy

import numpy as np
import matplotlib.pyplot as plt
p = np.array([2, -3, 1, -5])
p_der = np.polyder(p)
x = np.linspace(-2, 3, 100)
y = np.polyval(p, x)
y_der = np.polyval(p_der, x)
plt.plot(x, y, label='Polynomial')
plt.plot(x, y_der, label='Derivative')
plt.legend()
plt.show()

A Plots polynomial and derivative curves correctly with labels.

B Plots only polynomial curve, derivative missing.

C Plots derivative curve only, polynomial missing.

D Raises error due to wrong np.polyder usage.

💡 Hint

np.polyder returns coefficients of the derivative polynomial.

Option A correctly uses np.polyder and plots both polynomial and its derivative with labels.

🔧 Debug

advanced

Identify error in polynomial multiplication code

What error does this code raise when multiplying two polynomials using np.polymul incorrectly?

NumPy

import numpy as np
p1 = [1, 2]
p2 = (3, 4)
result = np.polymul(p1, p2)
print(result)

A TypeError: polymul() missing 1 required positional argument

B SyntaxError: invalid syntax

C No error, outputs [3, 10, 8]

D TypeError: polymul() argument 2 must be array-like, not tuple

💡 Hint

Check the data types of the polynomial coefficient inputs.

p2 is a tuple, but np.polymul expects array-like (list or np.array). Passing a tuple causes TypeError.

🚀 Application

expert

Find roots of polynomial from coefficients

Given polynomial coefficients [1, -6, 11, -6], which option correctly finds all roots using np.roots?

NumPy

import numpy as np
coeffs = [1, -6, 11, -6]
roots = np.roots(coeffs)
print(sorted(roots))

A [1.0, 2.0, 3.0]

B [-3.0, 1.0, 2.0]

C [3.0, 2.0, 1.0]

D Raises ValueError due to invalid coefficients

💡 Hint

np.roots returns roots in any order; sorting helps compare.

Polynomial is (x-1)(x-2)(x-3), roots are 1, 2, 3. Sorted roots are [1.0, 2.0, 3.0].