NCERT Class 10 Maths — Chapter 2

Exercise 2.1: Zeroes of a Polynomial from Graphs

A quick exercise where you read graphs and count how many times the curve crosses the x-axis. Each crossing is a zero of the polynomial.

zeroes from graphnumber of zeroesx-axis intersections
1
NCERT Questions
10
Practice MCQs
3
Key Concepts
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Extra Practice Questions

These questions cover the same concepts as Exercise 2.1. Try solving them to build confidence before or after the textbook exercise.

1

If 'k' is a zero of the polynomial P(x) = ax² + bx + c, which of the following statements must be true?

A.P(k) = 0
B.P(0) = k
C.P(k) = c
D.P(x) = k
2

If one zero of the quadratic polynomial x² + (a+1)x + b is 2 and the sum of its zeros is -1, then the values of 'a' and 'b' respectively are:

A.a = 0, b = -6
B.a = -2, b = -6
C.a = 0, b = 2
D.a = -4, b = 6
3

Which of the following statements about the number of zeros of a polynomial is true?

A.A polynomial of degree 'n' always has 'n' distinct real zeros.
B.A polynomial of degree 'n' can have at most 'n' real zeros.
C.A polynomial of degree 'n' must have at least one real zero.
D.A polynomial of degree 'n' can have more than 'n' real zeros.
4

Ravi states that for the quadratic polynomial 3x² - 5x + 2, the sum of its zeros is 5/3 and the product of its zeros is 2/3. Which part of his reasoning is incorrect, if any?

A.The sum of zeros is incorrect.
B.The product of zeros is incorrect.
C.Both are incorrect.
D.Both are correct.
5

If x - 2 is a factor of the polynomial p(x) = x³ - 4x² + 9x - 10, then which of the following describes the other factors/zeros of the polynomial?

A.The other factor is x² - 2x + 5, and its zeros are real and distinct.
B.The other factor is x² - 2x + 5, and its zeros are real and equal.
C.The other factor is x² - 2x + 5, and its zeros are complex.
D.The other factor is x² + 2x + 5, and its zeros are complex.
6

If α and β are the zeros of the quadratic polynomial f(x) = x² - 5x + 4, then the value of α² + β² is:

A.17
B.21
C.9
D.25
7

If one zero of the quadratic polynomial f(x) = (k² + 4)x² + 13x + 4k is the reciprocal of the other, find the value of k.

A.2
B.-2
C.4
D.-4
8

Find the zeros of the quadratic polynomial `6x² - 7x - 3`.

A.(3/2, -1/3)
B.(-3/2, 1/3)
C.(1/2, -3/2)
D.(-1/2, 3/2)
9

Consider the polynomial P(x) = ax² + bx + c. If P(x) has no real zeros, then which of the following must be true?

A.b² - 4ac < 0
B.c has the same sign as a
C.a+b+c > 0
D.Both b² - 4ac < 0 and c has the same sign as a
10

If the sum of the zeros of the polynomial 2x² - (3k-1)x + 5 is equal to their product, find the value of k.

A.1
B.2
C.3
D.4
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Common Mistakes to Avoid

  • ✗Counting points where the curve touches but doesn't cross the x-axis
  • ✗Confusing the y-intercept with a zero

Other Exercises in Chapter 2

Exercise 2.1
Zeroes of a Polynomial from Graphs
Exercise 2.2
Relationship Between Zeroes and Coefficients
Exercise 2.3
Division Algorithm for Polynomials

Frequently Asked Questions

How many questions are in Exercise 2.1?

Exercise 2.1 has 1 question with 6 sub-parts — each shows a polynomial graph and asks you to find the number of zeroes.

Want to practise on paper? Download a free worksheet for this topic.

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