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 in :
The term

is the constant term. In the equation

, the constant term is

Answer: b. 2

ii. If one of the zeroes of the quadratic polynomial is , then the value of is:
Since

is a zero, substituting

into the polynomial must equal

Answer: b. -10

iii. If are the zeroes of the polynomial , then equals:
From the polynomial, sum of zeroes

and product of zeroes

.
The expression is

Answer: d. -3/7

iv. The H.C.F. and L.C.M. . What is the value of ?
Using the property:

Answer: b. 54

v. If the H.C.F of two numbers is , then the two numbers are called:
Numbers with an HCF of

are called co-primes.

Answer: c. Co-primes

vi. The pair of linear equations and has:
Check the ratios of coefficients:

.
Since

, the lines intersect at exactly one point.

Answer: c. one unique solution

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).

Answer: c. no solutions

viii. The value of for which the system of linear equations and is inconsistent is:
For inconsistency,

.
Note: rewrite second eq as

.
Check third ratio:

(True).

Answer: d. 10

ix. The largest number which divides and , leaving remainders and , respectively, is:
Find the HCF of

and

Answer: a. 13

x. The graph of a polynomial of degree intersects the X-axis at most ______ points:
A polynomial of degree

can have at most

zeroes (intersections with X-axis).

Answer: b. 3

Assertion and Reason Questions

Q2. Assertion (A): The degree of polynomial is .
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: d. Assertion (A) is false but Reason ® is true.

Q3. Assertion (A): Degree of a zero polynomial is not defined.
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: b. Both Assertion (A) and Reason ® are true but Reason ® is not the correct explanation of Assertion (A).

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