source: ncert_exercises
topic: algebra
class_level: class_9
chapter: ch2
exercise: ex2.1
difficulty: beginner
Class 9 | Ch2: Polynomials | Exercise 2.1
Q1. Which of the following expressions are polynomials in one variable? State reasons. (i) 4x² - 3x + 7 (ii) y² + √2 (iii) 3√t + t√2 (iv) y + 2/y (v) x¹⁰ + y³ + t⁵⁰ Answer: (i) 4x²-3x+7 → YES. All exponents of x are whole numbers (2,1,0). ✅ (ii) y²+√2 → YES. Only variable y, exponent 2 is whole number. √2 is constant. ✅ (iii) 3√t+t√2 = 3t^(1/2)+√2·t → NO. Exponent 1/2 is not a whole number. ✅ (iv) y+2/y = y+2y^(-1) → NO. Exponent -1 is not a whole number. ✅ (v) x¹⁰+y³+t⁵⁰ → NOT polynomial in ONE variable. Has three variables x,y,t. ✅
Q2. Write the coefficients of x² in each of the following: (i) 2+x²+x (ii) 2-x²+x³ (iii) (π/2)x²+x (iv) √2x-1 Answer: (i) 1. (ii) -1. (iii) π/2. (iv) 0 (no x² term). ✅
Q3. Give one example each of a binomial of degree 35 and monomial of degree 100. Answer: Binomial of degree 35: x³⁵+1 (two terms, highest degree 35). Monomial of degree 100: x¹⁰⁰ (one term, degree 100). ✅
Q4. Write the degree of each polynomial: (i) 5x³+4x²+7x (ii) 4-y² (iii) 5t-√7 (iv) 3 Answer: (i) Degree 3 (highest power of x). (ii) Degree 2. (iii) Degree 1. (iv) Degree 0 (constant). ✅
Q5. Classify as linear, quadratic or cubic: (i) x²+x (ii) x-x³ (iii) y+y²+4 (iv) 1+x (v) 3t (vi) r² (vii) 7x³ Answer: (i) Quadratic (degree 2). (ii) Cubic (degree 3). (iii) Quadratic (degree 2). (iv) Linear (degree 1). (v) Linear (degree 1). (vi) Quadratic (degree 2). (vii) Cubic (degree 3). ✅