| --- |
| source: ncert_exercises |
| topic: algebra |
| class_level: class_9 |
| chapter: ch2 |
| exercise: ex2.2 |
| difficulty: beginner |
| --- |
| |
| Class 9 | Ch2: Polynomials | Exercise 2.2 |
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| Q1. Find the value of the polynomial 5x-4xΒ²+3 at: (i) x=0 (ii) x=-1 (iii) x=2 |
| Answer: |
| p(x) = 5x - 4xΒ² + 3 |
| (i) p(0) = 0 - 0 + 3 = 3. β
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| (ii) p(-1) = 5(-1) - 4(-1)Β² + 3 = -5 - 4 + 3 = -6. β
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| (iii) p(2) = 5(2) - 4(4) + 3 = 10 - 16 + 3 = -3. β
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| Q2. Find p(0), p(1), p(2) for each polynomial: |
| (i) p(y) = yΒ²-y+1 (ii) p(t) = 2+t+2tΒ²-tΒ³ (iii) p(x) = xΒ³ (iv) p(x) = (x-1)(x+1) |
| Answer: |
| (i) p(0)=1, p(1)=1, p(2)=3. β
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| (ii) p(0)=2, p(1)=2+1+2-1=4, p(2)=2+2+8-8=4. β
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| (iii) p(0)=0, p(1)=1, p(2)=8. β
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| (iv) p(x)=xΒ²-1. p(0)=-1, p(1)=0, p(2)=3. β
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| Q3. Verify whether the following are zeroes of the polynomial: |
| (i) p(x)=3x+1, x=-1/3 (ii) p(x)=5x-Ο, x=4/5 (iii) p(x)=xΒ²-1, x=1 and x=-1 |
| (iv) p(x)=(x+1)(x-2), x=-1 and x=2 (v) p(x)=xΒ², x=0 |
| (vi) p(x)=lx+m, x=-m/l (vii) p(x)=3xΒ²-1, x=-1/β3 and x=2/β3 |
| Answer: |
| (i) p(-1/3)=3(-1/3)+1=-1+1=0. YES, -1/3 is a zero. β
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| (ii) p(4/5)=5(4/5)-Ο=4-Οβ 0. NO. β
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| (iii) p(1)=1-1=0 YES. p(-1)=1-1=0 YES. Both are zeroes. β
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| (iv) p(-1)=(-1+1)(-1-2)=0. YES. p(2)=(2+1)(2-2)=0. YES. β
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| (v) p(0)=0Β²=0. YES. β
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| (vi) p(-m/l)=l(-m/l)+m=-m+m=0. YES. β
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| (vii) p(-1/β3)=3(1/3)-1=0 YES. p(2/β3)=3(4/3)-1=4-1=3β 0 NO. β
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| 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 (aβ 0) (vii) p(x)=cx+d (cβ 0) |
| Answer: |
| (i) x+5=0 β x=-5. β
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| (ii) x-5=0 β x=5. β
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| (iii) 2x+5=0 β x=-5/2. β
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| (iv) 3x-2=0 β x=2/3. β
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| (v) 3x=0 β x=0. β
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| (vi) ax=0 β x=0. β
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| (vii) cx+d=0 β x=-d/c. β
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