Class 10 Maths Chapter 2 Polynomials MCQs Quiz

Are you finding the concepts of Chapter 2, ‘Polynomials,’ in Class 10 Maths a bit tricky? Are the relationships between zeroes and coefficients leaving you confused? There’s no need to worry anymore!

We’ve created the perfect tool for you: the Class 10 Maths Chapter 2 Polynomials MCQs Quiz. This free online test is designed to clarify the fundamental concepts of polynomials and help you get familiar with the types of questions asked in exams. Let’s dive into this Polynomials quiz and give your board exam preparation a solid start!

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Polynomials MCQs Quiz

Click the Start button to begin the quiz and attempt all questions within the given time. Read each MCQ carefully, select the correct option, and move forward to complete the quiz. Your score will appear at the end to help you check your preparation level..

Q1: What is the maximum number of zeroes of a quadratic polynomial?

A: 1
B: 2
C: 3
D: 4

Explanation: The maximum number of zeroes of a polynomial is equal to its degree.
A quadratic polynomial has degree 2, so it can have at most 2 zeroes.

Q2: The zeroes of the polynomial \( p(x) = x^2 – 5x + 6 \) are:

A: 2, 3
B: -2, -3
C: 2, -3
D: -2, 3

Explanation: To find the zeroes of the polynomial, set \( p(x) = 0 \).
\( x^2 – 5x + 6 = 0 \)
\( (x-2)(x-3) = 0 \)
So, \( x = 2 \) or \( x = 3 \).
The zeroes are 2 and 3.

Q3: If the sum of the zeroes of a quadratic polynomial is 5 and their product is 6, then the polynomial is:

A: \( x^2 + 5x + 6 \)
B: \( x^2 – 5x – 6 \)
C: \( x^2 – 5x + 6 \)
D: \( x^2 + 5x – 6 \)

Explanation: The standard form of a quadratic polynomial is \( x^2 \) – (sum of zeroes) \( x \) + product of zeroes.
Given: Sum of zeroes = 5, Product = 6.
So, the polynomial is \( x^2 – 5x + 6 \).

Q4: The zeroes of the polynomial \( p(x) = x^3 – 4x \) are:

A: 0, 2
B: 0, -2
C: 2, -2
D: 0, 2, -2

Explanation: \( p(x) = x^3 – 4x = x(x^2 – 4) = x(x-2)(x+2) \)
Set \( p(x) = 0 \): \( x = 0, x-2=0, x+2=0 \)
So, \( x = 0, 2, -2 \).
All three zeroes are 0, 2, and -2.

Q5: What is the sum of the zeroes of the quadratic polynomial \( 2x^2 – 8x + 6 \)?

A: 3
B: 4
C: 6
D: 8

Explanation: For a quadratic polynomial \( ax^2 + bx + c \), the sum of the zeroes is \( \frac{-b}{a} \).
Here, a=2, b=-8.
Sum of zeroes = \( \frac{-(-8)}{2} = \frac{8}{2} = 4 \).

Q6: What is the product of the zeroes of the quadratic polynomial \( 3x^2 + 5x – 2 \)?

A: \( -\frac{2}{3} \)
B: \( \frac{2}{3} \)
C: \( -\frac{5}{3} \)
D: \( \frac{5}{3} \)

Explanation: For a quadratic polynomial \( ax^2 + bx + c \), the product of the zeroes is \( \frac{c}{a} \).
Here, a=3, c=-2.
Product of zeroes = \( \frac{-2}{3} = -\frac{2}{3} \).

Q7: A quadratic polynomial whose zeroes are -3 and 4 is:

A: \( x^2 – x – 12 \)
B: \( x^2 + x – 12 \)
C: \( x^2 – x – 12 \)
D: \( x^2 + x + 12 \)

Explanation: Zeroes are -3 and 4.
Sum of zeroes = \( -3 + 4 = 1 \)
Product of zeroes = \( (-3) \times 4 = -12 \)
Quadratic polynomial: \( x^2 – (\text{sum})x + (\text{product}) = x^2 – (1)x + (-12) = x^2 – x – 12 \).

Q8: The zero of the polynomial \( p(x) = 2x + 3 \) is:

A: \( \frac{2}{3} \)
B: \( -\frac{2}{3} \)
C: \( \frac{3}{2} \)
D: \( -\frac{3}{2} \)

Explanation: To find the zero of the linear polynomial \( p(x) = 2x + 3 \), set \( p(x) = 0 \).
\( 2x + 3 = 0 \)
\( 2x = -3 \)
\( x = -\frac{3}{2} \).
Thus, the zero is \( -\frac{3}{2} \).

Q9: If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( x^2 – 7x + 10 \), then the value of \( \alpha + \beta \) is:

A: -7
B: 7
C: 10
D: -10

Explanation: For the quadratic polynomial \( x^2 – 7x + 10 \), a=1, b=-7, c=10.
Sum of zeroes \( \alpha + \beta = \frac{-b}{a} = \frac{-(-7)}{1} = 7 \).
Alternatively, factoring gives \( (x-2)(x-5) \), so zeroes are 2 and 5, and their sum is 7.

Q10: The zeroes of the polynomial \( x^2 – 3 \) are:

A: \( \sqrt{3}, -\sqrt{3} \)
B: 3, -3
C: \( \sqrt{3}, \sqrt{3} \)
D: 3, 0

Explanation: \( x^2 – 3 = 0 \)
\( x^2 = 3 \)
\( x = \pm \sqrt{3} \)
Thus, the zeroes are \( \sqrt{3} \) and \( -\sqrt{3} \).

Q11: The sum of the zeroes of a quadratic polynomial is \( \frac{1}{4} \) and their product is \( -\frac{1}{4} \). The polynomial is:

A: \( 4x^2 – x – 1 \)
B: \( 4x^2 + x – 1 \)
C: \( 4x^2 – x – 1 \)
D: \( 4x^2 + x + 1 \)

Explanation: Sum of zeroes = \( \frac{1}{4} \), Product = \( -\frac{1}{4} \)
Quadratic polynomial: \( x^2 – (\text{sum})x + (\text{product}) = x^2 – \frac{1}{4}x – \frac{1}{4} \)
Multiplying the entire polynomial by 4: \( 4x^2 – x – 1 \).
Thus, the polynomial is \( 4x^2 – x – 1 \).

Q12: The graph of the polynomial \( p(x) = x^2 + 2x + 1 \) cuts the y-axis at the point:

A: (0, -1)
B: (0, 1)
C: (1, 0)
D: (-1, 0)

Explanation: The graph of a polynomial cuts the y-axis at the point where x=0.
\( p(0) = (0)^2 + 2(0) + 1 = 1 \)
Thus, the point of intersection with the y-axis is (0, 1).

Q13: If 2 is a zero of the polynomial \( x^2 + kx + 6 \), then the value of k is:

A: 5
B: -5
C: 6
D: -5

Explanation: Since 2 is a zero of the polynomial, substituting x=2 makes the polynomial zero.
\( (2)^2 + k(2) + 6 = 0 \)
\( 4 + 2k + 6 = 0 \)
\( 2k + 10 = 0 \)
\( 2k = -10 \)
\( k = -5 \).
Thus, the value of k is -5.

Q14: What is the maximum number of zeroes a cubic polynomial can have?

A: 3
B: 2
C: 1
D: 4

Explanation: The maximum number of zeroes of a polynomial is equal to its degree.
A cubic polynomial has degree 3, so it can have at most 3 zeroes.

Q15: The sum of the zeroes of the quadratic polynomial \( 6x^2 – 3 – 7x \) is:

A: \( \frac{7}{6} \)
B: \( -\frac{7}{6} \)
C: \( \frac{7}{6} \)
D: \( \frac{3}{6} \)

Explanation: First, write the polynomial in standard form \( ax^2 + bx + c \): \( 6x^2 – 7x – 3 \).
Here, a=6, b=-7.
Sum of zeroes = \( \frac{-b}{a} = \frac{-(-7)}{6} = \frac{7}{6} \).

Quiz Results

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Class 10 Maths Chapter 2 Polynomials MCQs Quiz

Chapter 2, ‘Polynomials,’ is a crucial part of the Class 10 algebra curriculum. In this chapter, you will learn about the definition of a polynomial, its degree, and various types of polynomials (linear, quadratic, and cubic). You will explore the Geometrical Meaning of the Zeroes of a Polynomial, which are the points where the graph of the polynomial intersects the x-axis. The most significant part of this chapter is understanding the Relationship between zeroes and coefficients of a polynomial and the Division Algorithm for Polynomials, which helps in finding factors without long division. These topics are essential for the CBSE Class 10 Maths Quiz and your board exams.

Conclusion

Scoring well in ‘Polynomials’ requires a deep understanding of concepts and consistent practice. Our Class 10 Maths Chapter 2 Polynomials MCQs Quiz is your excellent companion on this learning journey. This quiz helps you strengthen your grip on key topics like the relationship between zeroes and coefficients and provides practice in solving questions accurately under time pressure. By solving these objective questions, you can identify your mistakes and gain the confidence to secure full marks in this chapter. Take this Free Online Maths Quiz for Class 10 and excel in your exams!

FAQs on Polynomials MCQs

1. Question: How many marks from the chapter Polynomials are asked in the board exam?
Answer: The chapter Polynomials typically carries 6-8 marks in the CBSE board exam, with questions ranging from MCQs to long-answer types.

2. Question: What is the most important formula in this chapter?
Answer: The most important formulas are the relationships between the zeroes (α and β) and the coefficients (a, b, c) of a quadratic polynomial: α + β = -b/a and αβ = c/a.

3. Question: Is this Polynomials quiz based on the NCERT syllabus?
Answer: Yes, our Polynomials Class 10 MCQ quiz is fully aligned with the NCERT curriculum and the CBSE syllabus.

4. Question: What is a zero of a polynomial?
Answer: A real number ‘k’ is called a zero of a polynomial p(x) if p(k) = 0. Geometrically, it is the x-coordinate of the point where the graph of p(x) intersects the x-axis.

5. Question: What is the Division Algorithm for Polynomials?
Answer: If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find unique polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x), where r(x) is either the zero polynomial or its degree is less than the degree of g(x).

6. Question: Is this online quiz free?
Answer: Yes, this Free Online Maths Quiz for Class 10 is absolutely free. You can take it anytime and anywhere for practice.

7. Question: How should I prepare this chapter for the board exam?
Answer: Start by understanding all concepts and formulas thoroughly. Then, solve the examples and exercise questions from the NCERT book. Finally, test your preparation with our Polynomials MCQs Online Test.

8. Question: How many zeroes does a linear polynomial have?
Answer: A linear polynomial has exactly one zero.

9. Question: Does this quiz include questions on the Division Algorithm?
Answer: Yes, this quiz includes important questions based on the Division Algorithm for Polynomials to help you master this crucial concept.

10. Question: What is the benefit of taking this online quiz?
Answer: This quiz helps you improve time management, check the accuracy of your formulas, and understand the exam pattern, which boosts your confidence and leads to better performance.

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