Polynomials Class 9 Assertion Reason Questions Maths Chapter 2

Q: Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies: Understand Each Statement Separately: Determine if each statement is true or false independently. Analyze the Relationship: If both statements are true, check if the reason correctly explains the assertion.

Q: Q9: What are the important keywords for CBSE Class 9 Maths Polynomials?

A9: List of important keywords given below – Algebraic Expression: Any expression that contains constants and variables, connected by some or all of the operations +, -, x, ÷. Polynomials: An algebraic expression in which the variables involved have only non-negative integral powers. Polynomials in one Variable: An algebraic expression which consist of only one type of variables in the entire expression. Degree of Polynomial: Highest power of a variable in the polynomial. Constant Polynomial: Polynomial of zero degree. Zero Polynomials: A polynomial consisting of one term, namely zero. Zeroes of a Polynomial: Let p(x) be a polynomial in one variable and ‘a’ be a real number such that the value of polynomial at x=a is zero i.e., p(a) = 0, then ‘a’ is said to be a zero polynomial of p(x). Remainder Theorem: Let p(x) be a polynomial having degree 1 or more than 1 and let ‘a’ be any real number. If p(x) is divided by (x-a), then remainder is p(a).

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Last Updated on November 12, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 9 maths. In this article, you will find assertion reason questions for CBSE Class 9 Maths Chapter 2 Polynomials. It is a part of Assertion Reason Questions for CBSE Class 9 Maths Series.

Chapter	Polynomials
Type of Questions	Assertion Reason Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	9
Subject	Maths
Useful for	Class 9 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 9 Maths Chapterwise Assertion Reason

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Table of Contents

Assertion Reason Questions on Polynomials

Questions:

Q. 1. Assertion (A): If $p(x)=x^2-4 x+3$, then 3 and 1 are the zeroes of the polynomial $p(x)$.
Reason (R): Number of zeroes of a polynomial cannot exceed its degree.

Q. 2. Assertion (A): The degree of the polynomial $(x-2)(x-3)(x+4)$ is 4.
Reason (R): The number of zeroes of a polynomial is the degree of that polynomial.

Q. 3. Assertion (A): Factorisation of the polynomial $\sqrt{3} x^2+11 x+6 \sqrt{3}$ is $(\sqrt{3} x+2)(x+\sqrt{3})$.
Reason (R): Factorisation of the polynomial $35 y^2+13 y-12$ is $(7 y-3)(5 y+4)$.

Solutions:

1. (b) Assertion (A): Given, $p(x)=x^2-4 x+3$

$$
\begin{aligned}
\Rightarrow \quad p(x) & =x^2-(3+1) x+3 \\
& =x^2-3 x-x+3 \\
& =x(x-3)-1(x-3) \\
& =(x-1)(x-3)
\end{aligned}
$$

For finding the zeroes, put $p(x)=0$

$$
\therefore(x-1)(x-3)=0 \Rightarrow x=1,3
$$

So, Assertion (A) is true.
Reason (R): It is true to say that the number of zeroes of a polynomial cannot exceed its degree. Hence, both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

2. (d) Assertion (A): $p(x)=(x-2)(x-3)(x+4)$

$$
\begin{aligned}
& =(x-2)\left[x^2+4 x-3 x-12\right] \\
& =(x-2)\left(x^2+x-12\right) \\
& =x^3+x^2-12 x-2 x^2-2 x+24 \\
p(x) & =x^3-x^2-14 x+24
\end{aligned}
$$

So, degree of $p(x)=3$.
Hence, Assertion (A) is false, but Reason (R) is true.

3. (d) Assertion (A):

$$
\begin{aligned}
\left(\sqrt{3} x^2+11 x+6 \sqrt{3}\right) & =\sqrt{3} x^2+9 x+2 x+6 \sqrt{3} \\
& =\sqrt{3} x(x+3 \sqrt{3})+2(x+3 \sqrt{3}) \\
& =(x+3 \sqrt{3})(\sqrt{3} x+2)
\end{aligned}
$$

So, Assertion (A) is false.
Reason (R):

$$
\begin{aligned}
\left(35 y^2+13 y-12\right) & =35 y^2+28 y-15 y-12 \\
& =7 y(5 y+4)-3(5 y+4) \\
& =(5 y+4)(7 y-3)
\end{aligned}
$$

So, Reason (R) is true.

Also check

Topics from which assertion reason questions may be asked

Definition of a polynomial in one variable, with examples and counter examples.
Coefficients of a polynomial
Terms of a polynomial and zero polynomial.
Degree of a polynomial.
Constant, linear, quadratic and cubic polynomials.
Monomials, binomials, trinomials.
Factors and multiples.
Zeros of a polynomial.
Remainder Theorem with examples.

Linear polynomial can be monomial or binomial.

Quadratic polynomial can be monomial, binomial or trinomial.

The degree of a zero polynomial is not defined.

Assertion reason questions from the above given topic may be asked.

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Frequently Asked Questions (FAQs) on Polynomials Assertion Reason Questions Class 9

Q1: What are assertion reason questions?

A1: Assertion-reason questions consist of two statements: an assertion (A) and a reason (R). The task is to determine the correctness of both statements and the relationship between them. The options usually include:
(i) Both A and R are true, and R is the correct explanation of A.
(ii) Both A and R are true, but R is not the correct explanation of A.
(iii) A is true, but R is false.
(iv) A is false, but R is true. or A is false, and R is also false.

Q2: Why are assertion reason questions important in Maths?

A2: Students need to evaluate the logical relationship between the assertion and the reason. This practice strengthens their logical reasoning skills, which are essential in mathematics and other areas of study.

Q3: How can practicing assertion reason questions help students?

A3: Practicing assertion-reason questions can help students in several ways:
Improved Conceptual Understanding: It helps students to better understand the concepts by linking assertions with their reasons.
Enhanced Analytical Skills: It enhances analytical skills as students need to critically analyze the statements and their relationships.
Better Exam Preparation: These questions are asked in exams and practicing them can improve your performance.

Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies:
Understand Each Statement Separately: Determine if each statement is true or false independently.
Analyze the Relationship: If both statements are true, check if the reason correctly explains the assertion.

Q5: What are common mistakes to avoid when answering Assertion Reason questions?

A5: Common mistakes include:
Not reading the statements carefully and missing key details.
Assuming the Reason explains the Assertion without checking the logical connection.
Confusing the order or relationship between the statements.
Overthinking and adding information not provided in the question.

Q6: How many types of polynomials are there?

A6: Polynomials are classified based on the number of terms they have:
Monomial: A polynomial with just one term.
Binomial: A polynomial with two terms.
Trinomial: A polynomial with three terms
Multinomial: A polynomial with more than three terms

Q7: What is the degree of a polynomial?

A7: The degree of a polynomial is the highest power of the variable in the polynomial.

Q8: What are the key concepts covered in Chapter 2 of CBSE Class 9 Maths regarding polynomials?

A8: Chapter 2 of CBSE Class 9 Maths covers concepts such as understanding polynomials and its types.
(i) Types of polynomials
(ii) Terms and coefficient of polynomials
(iii) Zeroes of a polynomial
(iv) Division algorithm
(v) Remainder theorem
(vi) Factor theorem
(vii) Factorisation of quadratic polynomial

Q9: What are the important keywords for CBSE Class 9 Maths Polynomials?

A9: List of important keywords given below –
Algebraic Expression: Any expression that contains constants and variables, connected by some or all of the operations +, -, x, ÷.
Polynomials: An algebraic expression in which the variables involved have only non-negative integral powers.
Polynomials in one Variable: An algebraic expression which consist of only one type of variables in the entire expression.
Degree of Polynomial: Highest power of a variable in the polynomial.
Constant Polynomial: Polynomial of zero degree.
Zero Polynomials: A polynomial consisting of one term, namely zero.
Zeroes of a Polynomial: Let p(x) be a polynomial in one variable and ‘a’ be a real number such that the value of polynomial at x=a is zero i.e., p(a) = 0, then ‘a’ is said to be a zero polynomial of p(x).
Remainder Theorem: Let p(x) be a polynomial having degree 1 or more than 1 and let ‘a’ be any real number. If p(x) is divided by (x-a), then remainder is p(a).

Q10: Are there any online resources or tools available for practicing polynomials assertion reason questions?

A10: A9: We provide assertion reason questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient assertion reason questions and prepare for their exams. If you need more assertion reason questions, then you can visit Physics Gurukul website. they are having a large collection of assertion reason questions for all classes.