Class 9 Mathematics Chapter 2 Introduction to Linear Polynomials – Extra Questions with Answers

Extra practice questions for Class 9 Maths Chapter 2 (Introduction to Linear Polynomials), beyond the textbook. These Class 9 Mathematics Chapter 2 important questions are handy for last-minute exam practice.

Very Short Answer Questions (1 mark)

Q1. Find the zero of the linear polynomial p(x) = x − 5.
Ans: x = 5.

Q2. What is the degree of the polynomial 7x + 2?
Ans: 1 (linear).

Q3. Is 3x² + 2 a linear polynomial? Why or why not?
Ans: No, its degree is 2 (quadratic), not 1.

Q4. Find the zero of p(x) = 2x + 6.
Ans: x = −3.

Q5. What is the graph of a linear polynomial called?
Ans: A straight line.

Short Answer Questions (2–3 marks)

Q6. Find the zero of the linear polynomial p(x) = 4x − 12, and verify your answer by substitution.
Ans: Setting 4x − 12 = 0 gives x = 3. Verification: p(3) = 4(3) − 12 = 12 − 12 = 0. Correct.

Q7. Explain why every linear polynomial (of the form ax + b, a ≠ 0) has exactly one zero.
Ans: Setting ax + b = 0 and solving gives a single unique value, x = −b/a (since a ≠ 0, we can always divide). Because this is a straight-line equation, there is only one solution — the line crosses the x-axis at exactly one point.

Q8. If p(x) = 3x − 9, find p(0), p(3), and p(5), and state which of these is a zero of the polynomial.
Ans: p(0) = 3(0) − 9 = −9; p(3) = 3(3) − 9 = 0; p(5) = 3(5) − 9 = 6. Since p(3) = 0, x = 3 is the zero of the polynomial.

Higher-Order Thinking / Application Questions

Q9. A linear polynomial p(x) = ax + b has a zero at x = 4, and p(0) = −8. Find the values of a and b.
Ans: Since p(0) = −8: a(0) + b = −8, so b = −8. Since x = 4 is a zero: a(4) + b = 0, so 4a − 8 = 0, giving a = 2. So p(x) = 2x − 8.

Q10. The cost of a taxi ride is modelled by the linear polynomial C(x) = 15x + 40, where x is the distance in km and C is the cost in rupees. If a customer paid ₹190 for a ride, find the distance travelled, and explain what the ’40’ represents in real-world terms.
Ans: Setting C(x) = 190: 15x + 40 = 190, so 15x = 150, giving x = 10 km. The constant term ’40’ represents the base fare charged even before any distance is travelled (i.e. C(0) = 40), such as a fixed pickup or booking charge.

Written by Satish

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