knowledge-base/class_9/ch2/0125_algebra.md

metadata

source: ncert_exercises
topic: algebra
class_level: class_9
chapter: ch2
exercise: ex2.2
difficulty: beginner

Class 9 | Ch2: Polynomials | Exercise 2.2

Q1. Find the value of the polynomial 5x-4x²+3 at: (i) x=0 (ii) x=-1 (iii) x=2 Answer: p(x) = 5x - 4x² + 3 (i) p(0) = 0 - 0 + 3 = 3. ✅ (ii) p(-1) = 5(-1) - 4(-1)² + 3 = -5 - 4 + 3 = -6. ✅ (iii) p(2) = 5(2) - 4(4) + 3 = 10 - 16 + 3 = -3. ✅

Q2. Find p(0), p(1), p(2) for each polynomial: (i) p(y) = y²-y+1 (ii) p(t) = 2+t+2t²-t³ (iii) p(x) = x³ (iv) p(x) = (x-1)(x+1) Answer: (i) p(0)=1, p(1)=1, p(2)=3. ✅ (ii) p(0)=2, p(1)=2+1+2-1=4, p(2)=2+2+8-8=4. ✅ (iii) p(0)=0, p(1)=1, p(2)=8. ✅ (iv) p(x)=x²-1. p(0)=-1, p(1)=0, p(2)=3. ✅

Q3. Verify whether the following are zeroes of the polynomial: (i) p(x)=3x+1, x=-1/3 (ii) p(x)=5x-π, x=4/5 (iii) p(x)=x²-1, x=1 and x=-1 (iv) p(x)=(x+1)(x-2), x=-1 and x=2 (v) p(x)=x², x=0 (vi) p(x)=lx+m, x=-m/l (vii) p(x)=3x²-1, x=-1/√3 and x=2/√3 Answer: (i) p(-1/3)=3(-1/3)+1=-1+1=0. YES, -1/3 is a zero. ✅ (ii) p(4/5)=5(4/5)-π=4-π≠0. NO. ✅ (iii) p(1)=1-1=0 YES. p(-1)=1-1=0 YES. Both are zeroes. ✅ (iv) p(-1)=(-1+1)(-1-2)=0. YES. p(2)=(2+1)(2-2)=0. YES. ✅ (v) p(0)=0²=0. YES. ✅ (vi) p(-m/l)=l(-m/l)+m=-m+m=0. YES. ✅ (vii) p(-1/√3)=3(1/3)-1=0 YES. p(2/√3)=3(4/3)-1=4-1=3≠0 NO. ✅

Q4. Find zero of the polynomial: (i) p(x)=x+5 (ii) p(x)=x-5 (iii) p(x)=2x+5 (iv) p(x)=3x-2 (v) p(x)=3x (vi) p(x)=ax (a≠0) (vii) p(x)=cx+d (c≠0) Answer: (i) x+5=0 → x=-5. ✅ (ii) x-5=0 → x=5. ✅ (iii) 2x+5=0 → x=-5/2. ✅ (iv) 3x-2=0 → x=2/3. ✅ (v) 3x=0 → x=0. ✅ (vi) ax=0 → x=0. ✅ (vii) cx+d=0 → x=-d/c. ✅