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Quadratic Polynomials and Linear Equations: Unit Test for Class X Mathematics
Published on July 28, 2026
Algebra
Solve multiple-choice questions covering quadratic polynomials, linear equations, HCF, LCM, and polynomial degrees in this Class X Mathematics unit test.
Question
Make the answer key and highlight the answers in green colour
Answer
To solve the math problems presented in the image, we will go through each question step-by-step.
Section A (Multiple Choice Questions)
i. Find the coefficient of
The term
The term
- Answer: <span style=“color:green”>b. 2</span>
ii. If one of the zeroes of the quadratic polynomial
Since
Since
- Answer: <span style=“color:green”>b. -10</span>
iii. If
From the polynomial, sum of zeroes
The expression is
From the polynomial, sum of zeroes
The expression is
- Answer: <span style=“color:green”>d. -3/7</span>
iv. The H.C.F.
Using the property:
Using the property:
- Answer: <span style=“color:green”>b. 54</span>
v. If the H.C.F of two numbers is
Numbers with an HCF of
Numbers with an HCF of
- Answer: <span style=“color:green”>c. Co-primes</span>
vi. The pair of linear equations
Check the ratios of coefficients:
Since
Check the ratios of coefficients:
Since
- Answer: <span style=“color:green”>c. one unique solution</span>
vii. A system of simultaneous linear equations is said to be inconsistent, if it has:
An inconsistent system is one that has no solution (parallel lines).
An inconsistent system is one that has no solution (parallel lines).
- Answer: <span style=“color:green”>c. no solutions</span>
viii. The value of
For inconsistency,
Note: rewrite second eq as
Check third ratio:
For inconsistency,
Note: rewrite second eq as
Check third ratio:
- Answer: <span style=“color:green”>d. 10</span>
ix. The largest number which divides
Find the HCF of
Find the HCF of
- Answer: <span style=“color:green”>a. 13</span>
x. The graph of a polynomial of degree
A polynomial of degree
A polynomial of degree
- Answer: <span style=“color:green”>b. 3</span>
Assertion and Reason Questions
Q2. Assertion (A): The degree of polynomial
Reason ®: The number of zeroes of a polynomial is the degree of that polynomial.
Reason ®: The number of zeroes of a polynomial is the degree of that polynomial.
- Analysis:
is a product of three linear terms, so its degree is , not . Thus, (A) is false. ® is generally true for polynomials where all roots are real and distinct, but in the context of standard definitions, the number of zeroes is at most the degree. However, since (A) is definitely false, we look at option (d). - Answer: <span style=“color:green”>d. Assertion (A) is false but Reason ® is true.</span>
Q3. Assertion (A): Degree of a zero polynomial is not defined.
Reason ®: Degree of a non-zero constant polynomial is
Reason ®: Degree of a non-zero constant polynomial is
- Analysis: Both statements are mathematically correct standard definitions. The reason explains the nature of constant polynomials, but it doesn’t directly explain why the zero polynomial’s degree is undefined (which is because
for any ). However, in many textbook contexts, these are treated as independent true statements. - Answer: <span style=“color:green”>b. Both Assertion (A) and Reason ® are true but Reason ® is not the correct explanation of Assertion (A).</span>