
Diophantine Equations and Integer Solutions Quiz

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard
Jennifer Brown
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a Diophantine equation primarily concerned with?
Finding integer solutions
Finding real number solutions
Finding fractional solutions
Finding complex number solutions
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is an example of a Diophantine equation?
x^2 + 2x + 1 = 0
2^z - z^5 = 17z
pi*x^2 + 3x - sqrt(2) = 0
x^2 + y^2 = z^2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving a polynomial Diophantine equation?
Graph the equation
Get all terms on one side and sort by degree
Check for complex solutions
Find the real solutions
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to write polynomials in standard form?
To make them easier to graph
To ensure all coefficients are integers
To identify the largest degree term
To find complex solutions
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key principle when solving equations involving products of factors?
All factors must be non-zero
At least one factor must be a fraction
At least one factor must be zero
All factors must be integers
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of Diophantine equations, why is zero often checked as a solution?
Zero is a complex number
Zero is a common integer solution
Zero simplifies the equation
Zero is always a solution
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the clever trick used to find non-zero integer solutions?
Graphing the equation
Checking divisors of the constant term
Using complex numbers
Finding fractional solutions
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