Assertion & Reason Questions For Math Class 10 | Polynomials

ASSERTION & REASON QUESTIONS CLASS 10 
CHAPTER 2  POLYNOMIALS

Competency based questions on polynomial class 10 chapter 2 , Assertion and Reason based questions for class 10 polynomial chapter 2

 To introduce assertion and reason-based questions in classroom teaching, you can follow these steps:

Begin by explaining the concept of polynomials: 

Start the lesson by providing a brief overview of polynomials and their basic definitions. Cover key terms like degree, coefficient, variable, and constant term.

Introduce assertion and reason format: 

Explain to the students that an assertion and reason question requires them to evaluate two statements. The first statement is the assertion, which is a given statement, and the second statement is the reason, which explains or justifies the assertion.

Provide an example assertion and reason question: 

Present a sample assertion and reason question related to polynomials.

Analyze the given statements: 

Ask the students to evaluate the assertion and reason independently. Encourage them to determine whether the assertion is true or false and whether the reason correctly justifies the assertion.

Discuss the correct answer: 

Lead a class discussion to reveal the correct answer and explain the reasoning behind it.

Practice more examples: 

Provide additional assertion and reason questions on polynomials for the students to solve individually or in groups. Ensure that the questions cover various concepts related to polynomials, such as degree, roots, factorization, and operations.

Students and teachers can make use of the following Assertion and Reason based question given below

ASSERTION & REASON BASED QUESTION

1) Assertion: If the degree of a polynomial is 'n', then the polynomial can have at most 'n' distinct real roots.

Reasoning: The number of distinct real roots of a polynomial is equal to its degree.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Answer: a

2) Assertion: A polynomial of degree 3 can have at most three roots.

Reasoning: The fundamental theorem of algebra states that a polynomial of degree 'n' has exactly 'n' roots.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Answer: c

3) Assertion: If a polynomial is divided by (x – a) and leaves a remainder zero, then 'a' is a root of the polynomial.

Reasoning: The remainder theorem states that if a polynomial P(x) is divided by x - a and leaves a remainder zero, then 'a' is a root of P(x).

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer a

4) Assertion: A polynomial of odd degree can have at least one real root.

Reasoning: A polynomial of odd degree can have both real and complex roots.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Answer: a

5) Assertion: If a polynomial P(x) is divided by (x - a), where 'a' is a real number, and the quotient is a polynomial Q(x), then the degree of Q(x) is one less than the degree of P(x).

Reasoning: When a polynomial P(x) is divided by (x - a), the degree of the quotient is always one less than the degree of P(x).

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion .

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer: a

6) Assertion: A quadratic polynomial can have at the most two zeroes.

Reason: x^2+7x+12 has no real zeroes.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer c

7) Assertion: If the sum of the zeroes of the quadratic polynomial  x² - 2kx + 8 is 2 then value of k is 1.

Reason: Sum of zeroes of a quadratic polynomial ax² + bx + c is - b/a

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer a

8) Assertion: The highest power of x in the polynomial P(x) is the degree of the polynomial.

Reason: P(x) = 4x³ - x² + 5x⁴ + 3x - 2 is a polynomial of degree 3.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer c

9) Assertion: x³ + x has only one real zero.

Reason: A polynomial of nth degree must have n real zeroes

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: c) Assertion is correct but reason is false.

10) Assertion: If one zero of polynomial p(x) = (k² + 4)x² + 13x + 4k is reciprocal of the other, then k = 2.

Reason: If (x-a) is a factor of p(x), then p(a) = 0 i.e., a is a zero of p(x).

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: b) 

11) Assertion: Degree of a zero polynomial is not defined.

Reason: Degree of a non-zero constant polynomial is 0.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: b) 

12) Assertion: 

If the product of the zeroes of the quadratic polynomial x² + 3x + 5k is -10 then value of k is -2.

Reason: Sum of zeroes of a quadratic polynomial ax² + bx + c is - b/a

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: b)

13) Assertion: 3 - 2√5 is one zero of the quadratic polynomial then other zero will be 3 + 2√5.

Reason: Irrational zeros (roots) always occurs in pairs.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion .

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer a

14) Assertion: y² + 6y + 9 has two zeros
Reason (R): A quadratic Polynomial can have at most two zeros.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Answer a

15) Assertion:  x + 1is a Linear Polynomial

Reason (R): The polynomials of degree 1 are called linear polynomials.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a)

16) Assertion: 3x³ + 3x² + 3x + 3 is a cubic polynomial.

Reason: If the number ‘3’ is multiplied in all the terms of a polynomial then it is called a cubic polynomial.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: c) Assertion is correct but reason is false

17) Assertion: -1& -4 are the zeroes of polynomial x² - 3x - 4

Reason: a real number k is said to be a zero of polynomial P(x) if P(K) =  0

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.

18) Assertion: The number of zeros that a polynomial can have is equal to the degree of the polynomial.

Reason: the polynomial x⁵ - x⁴ - 2x³ + x² - 1 has four zeroes

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: c) 

19) Assertion: the graph of quadratic polynomial P(x) intersect x-axis at two point

Reason: degree of quadratic polynomial is 2

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: a ) 
20) Assertion: the graph of polynomial intersect x-axis at 3 points and y-axis at 1 points the polynomial has 3 zeroes

Reason: the number of zeroes that a polynomial P(x) can have is the number of times polynomial intersect x and y axis

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: c) 

21) Assertion: The graph of a polynomial p(x) is a straight line parallel to x axis. The polynomial has no zeros.

Reason (R): If a polynomial P(x) does not intersect the x-axis at any point, it does not have any zero.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a ) 

22) Assertion: The graph of a quadratic polynomial P(x)intersects the x-axis at two points.

Reason (R): The graph of a quadratic polynomial is a parabola.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: b ) 

23) Assertion: (2 - √3 ) is one zero of quadratic polynomial then other zero will be 2 + √3

Reason: irrational zeroes always occur in pair

a)(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: a ) 

24) Assertion: zeroes of f(x)= x² - 4x - 5 are 5, -1

Reason: the polynomial whose zeroes are 2 + √3, 2 - √3 is x² - 4x + 7

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: c) Assertion is correct but reason is false

25) Assertion: The graph y =f(x) is shown in figure, for the polynomial f( x) The number of zeros of f( x) = 4.

Reason : The number of zero of the polynomial f (x) is the number of point of which f (x)cuts or touches the axes.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: d)

26) Assertion: the degree of polynomial 2x - 1 is 1

Reason: polynomial the degree is the value of highest power of the variable.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.

Ans: a ) 

27) Assertion: x²⁰ + 1 is a binomial

Reason: If an expression contains two unlike terms, then it is called as a binomial.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a ) 

28) Assertion: a polynomial having variable with two constant value is called constant polynomial

Reason: a constant polynomial has highest degree is 2

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: d) 
29) Assertion: The polynomials in which the highest power of the variable is two are known as Quadratic polynomials.

Reason: P(x)=ax² + bx + c is a quadratic polynomial

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a ) 

30) Assertion: the coefficient of x in the expansion of (x + 3)³ is 27

Reason: (a + b)³= a³ + b³ + 3a²b + 3ab²

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a ) 

31) Assertion : A polynomial of degree n has at most n zeroes

Reason: Maximum number of zeroes of a polynomial = degree of the polynomial.

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a ) 

32) Assertion: if x⁶ + 1 is divided by x – 1, then the remainder is 2.

Reason: p(x) = x⁶ + 1 when divided by x – 1, then remainder = p(1)

p(1) = 1⁶ + 1 = 2

(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion .

(c) Assertion is true but Reason is false.

(d) Assertion is false but Reason is true.
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion

33) Assertion: Zeroes of p(z) = z² – 27 are √3and -√3

Reason: For zeroes z² – 27 = 0, z² = 27

z = ±√27   ⇒  z = ± 3√3

a)Both assertion and reason are true and reason is the correct explanation of assertion

b) Both assertion and reason are true but reason is not the correct explanation of assertion

C) Assertion is true but reason is false.

d) both Assertion and reason are false

Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion

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