EXERCISE 2.1[অনুশীলনী - 2.1 ]
1.Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer . [তলৰ কোনকেইটা ৰাশি এটা চলকযুক্ত বহুপদ আৰু কোনকেইটা নহয় ? তোমাৰ উত্তৰৰ যুক্তি দিয়া ৷]
\[(i)4x^{2}-3x+7\]
\[(ii)y^{2}+\sqrt{2}\]
\[(iii)3\sqrt{t}+t\sqrt{2}\]
\[(iv)y+\frac{2}{y}\]
\[(v)x^{10}+y^{3}+t^{50}\]
Solution : One Variable ( এটা চলকযুক্ত বহুপদ) : (i) , (ii)
Non -polynomials : (ii) , (iv) because the degree of the variables are not in whole number . [কাৰণ চলকৰ মাত্ৰাবোৰ পূৰ্ণসংখ্যা নহয় ৷ ]
2. Write the coeefficients of x2 in each of the following :[তলৰ প্ৰতিটোৰে x2 ৰ সহগ লিখা ৷]
\[(i)2+x^{2}+x\]
\[(ii)2-x^{2}+x^{3}\]
\[(iii)\frac{\pi }{2}x^{2}+x\]
\[(iv)\sqrt{2}x-1\]
Solution :
(i) 1
(ii) -1
\[(iii)\frac{\pi }{2}\]
(iv) 0
3. Give one example each of a binomial of degree 35 and of a monomial of degree 100.[35 মাত্ৰাযুক্ত এটা দ্বিপদ আৰু 100 মাত্ৰাযুক্ত এটা একপদৰ একোটাকে উদাহৰণ দিয়া৷ ]
Solution :
\[(i)x^{35}+1\]
\[(ii)x^{100}\]
4. Write the degree of each of the following polynomials:[তলৰ বহুপদবোৰৰ মাত্ৰা লিখাঃ]
\[(i)5x^{3}+4x^{2}+7x\]
\[(ii)4-y^{2}\]
\[(iii)5t-\sqrt{7}\]
\[(iv)3\]
Solution :
(i) 3
(ii) 2
(iii) 1
(iv) 0
5.Classify the following as linear , quadratic and cubic polynomials: [তলৰ ৰৈখিক ,দ্বিঘাত আৰু ত্ৰিঘাত বহুপদবোৰ শ্ৰেণী বিভাজন কৰাঃ]
\[(i)x^{2}+x\]
\[(ii)x-x^{3}\]
\[(iii)y+y^{2}+4\]
\[(iv)1+x\]
\[(v)3t\]
\[(vi)r^{2}\]
\[(vii)7x^{3}\]
Solution :
Linear [ৰৈখিক]: (iv) , (v)
quadratic[দ্বিঘাত]: (i) , (iii) , (vi)
cubic [ত্ৰিঘাত]: (ii) , (vii)
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