{"id":4219,"date":"2023-02-02T06:00:37","date_gmt":"2023-02-02T06:00:37","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4219"},"modified":"2023-02-02T06:04:11","modified_gmt":"2023-02-02T06:04:11","slug":"ncert-solutions-class-9-maths-chapter-2-polynomials-ex-2-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-2-polynomials-ex-2-1\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 2 Polynomials Ex 2.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 2 (Polynomials)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 2 Polynomials <\/strong>Exercise 2.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 2: Polynomials\u00a0<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-2-polynomials-ex-2-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 2.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-2-polynomials-ex-2-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 2.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-2-polynomials-ex-2-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 2.4<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-2-polynomials-ex-2-5\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 2.5<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 2.1\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Which of the following expressions are polynomials in one variable, and which are not? State reasons for your answer.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i) 4x<sup>2 <\/sup>\u2013 3x + 7<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(ii) y<sup>2 <\/sup>+ \u221a2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(iii) 3\u221at + t\u221a2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(iv) y + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{y}}\" alt=\"\\mathbf{\\frac{2}{y}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(v) x<sup>10 <\/sup>+ y<sup>3 <\/sup>+ t<sup>50<\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">Answer &#8211;<br \/>\n<\/span><\/strong><span style=\"color: #000000;\"><strong>(i) 4x<sup>2 <\/sup>\u2013 3x + 7<br \/>\n<\/strong>We have 4x<sup>2<\/sup>\u00a0\u2013 3x + 7 = 4x<sup>2<\/sup>\u00a0\u2013 3x + 7x<sup>0<\/sup><br \/>\nIt is <strong>a polynomial<\/strong> in one variable i.e., x, because each exponent of x is a whole number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) y<sup>2<\/sup>+\u221a2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">We have y<sup>2<\/sup>\u00a0+ \u221a2 = y<sup>2<\/sup>\u00a0+ \u221a2y<sup>0<\/sup><br \/>\nIt is <strong>a polynomial<\/strong> in one variable i.e., y, because each exponent of y is a whole number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 3\u221at + t\u221a2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">We have 3\u221at + t\u221a2 = 3 \u221at<sup>1\/2<\/sup>\u00a0+ \u221a2.t<br \/>\nIt is <strong>not a polynomial<\/strong>, because one of the exponents of t is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>, which is not a whole number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) y + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{y}}\" alt=\"\\mathbf{\\frac{2}{y}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">We have y + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{y}\" alt=\"\\frac{2}{y}\" align=\"absmiddle\" \/>\u00a0= y + 2.y<sup>-1<br \/>\n<\/sup>It is <strong>not a polynomial<\/strong>, because one of the exponents of y is -1, which is not a whole number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) x<sup>10 <\/sup>+ y<sup>3 <\/sup>+ t<sup>50<br \/>\n<\/sup><\/strong><\/span><span style=\"color: #000000;\">We have x<sup>10<\/sup>+\u00a0 y<sup>3\u00a0<\/sup>+ t<sup>50<br \/>\n<\/sup>Here, exponent of every variable is a whole number, but x<sup>10<\/sup>\u00a0+ y<sup>3<\/sup>\u00a0+ t<sup>50<\/sup> is a polynomial in x, y and t, i.e., in three variables. So, it is <strong>not a polynomial<\/strong> in one variable.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Write the coefficients of x<sup>2<\/sup> in each of the following.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i) 2 + x<sup>2 <\/sup>+ x<br \/>\n<\/strong><\/span><strong><span style=\"color: #000000;\">(ii) 2 \u2013 x<sup>2<\/sup>\u00a0+ x<sup>3<\/sup><br \/>\n(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{\\pi}{2}}\" alt=\"\\mathbf{\\frac{\\pi}{2}}\" align=\"absmiddle\" \/> x<sup>2<\/sup> + x<br \/>\n<\/span><\/strong><strong><span style=\"color: #000000;\">(iv) \u221a2 x \u2013 1<\/span><\/strong><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><br \/>\n<\/span><span style=\"color: #000000;\"><strong>(i) 2 + x<sup>2 <\/sup>+ x<br \/>\n<\/strong>The equation 2 + x<sup>2 <\/sup>+ x can be written as 2 + (1)x<sup>2 <\/sup>+ x.<br \/>\n<\/span><span style=\"color: #000000;\">The coefficient of x<sup>2<\/sup>\u00a0is 1.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 2\u2013x<sup>2<\/sup>+x<sup>3<br \/>\n<\/sup><\/strong><\/span><span style=\"color: #000000;\">The equation 2 \u2013 x<sup>2 <\/sup>+ x<sup>3\u00a0<\/sup>can be written as 2 + (\u20131)x<sup>2 <\/sup>+ x<sup>3<\/sup>.<br \/>\n<\/span><span style=\"color: #000000;\">The coefficient of x<sup>2<\/sup>\u00a0is -1.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{\\pi}{2}}\" alt=\"\\mathbf{\\frac{\\pi}{2}}\" align=\"absmiddle\" \/>x<sup>2 <\/sup>+ x<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The equation <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\pi&amp;space;}{2}\" alt=\"\\frac{\\pi }{2}\" align=\"absmiddle\" \/>x<sup>2\u00a0<\/sup>+ x.<br \/>\nThe coefficient of x<sup>2<\/sup> is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\pi&amp;space;}{2}\" alt=\"\\frac{\\pi }{2}\" align=\"absmiddle\" \/> .<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) \u221a2x &#8211; 1<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The equation \u221a2x &#8211; 1 can be written as 0x<sup>2 <\/sup>+ \u221a2x &#8211; 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [Since 0x<sup>2<\/sup> is 0]<br \/>\nThe coefficient of x<sup>2<\/sup>\u00a0is 0.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Give one example each of a binomial of degree 35 and of a monomial of degree 100.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>Answer &#8211;\u00a0<\/strong><\/span><span style=\"color: #000000;\"><strong>Binomial of degree 35 &#8211; <\/strong>A polynomial having two terms and the highest degree of 35 is called a binomial of degree 35. <\/span><span style=\"color: #000000;\"><strong>E.g., \u00a0<\/strong>3x<sup>35 <\/sup>+ 5<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Monomial of degree 100 &#8211;<\/strong> A polynomial having one term and the highest degree of 100 is called a monomial of degree 100.\u00a0<\/span><span style=\"color: #000000;\"><strong>E.g., \u00a0<\/strong>4x<sup>100<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Write the degree of each of the following polynomials.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i) 5x<sup>3 <\/sup>+ 4x<sup>2 <\/sup>+ 7x<br \/>\n(ii) 4 \u2013 y<sup>2<\/sup><br \/>\n(iii) 5t \u2013 \u221a7<br \/>\n(iv) 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><br \/>\n<\/span><span style=\"color: #000000;\"><strong>(i) 5x<sup>3 <\/sup>+ 4x<sup>2 <\/sup>+ 7x<br \/>\n<\/strong>The given polynomial is 5x<sup>3<\/sup>\u00a0+ 4x<sup>2<\/sup> + 7x.<br \/>\nThe highest power of the variable x is 3.<br \/>\nSo, the degree of the polynomial is 3.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 4 \u2013 y<sup>2<br \/>\n<\/sup><\/strong><\/span><span style=\"color: #000000;\">The given polynomial is 4- y<sup>2<\/sup>. The highest<br \/>\npower of the variable y is 2.<br \/>\nSo, the degree of the polynomial is 2.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 5t \u2013 \u221a7<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The given polynomial is 5t \u2013 \u221a7 . The highest power of variable t is 1. So, the degree of the polynomial is 1.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">Since, 3 = 3x\u00b0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[\u2235 x\u00b0 = 1]<br \/>\nSo, the degree of the polynomial is 0.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Classify the following as linear, quadratic and cubic polynomials.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i) x<sup>2<\/sup>+ x<br \/>\n(ii) x \u2013 x<sup>3<\/sup><br \/>\n(iii) y + y<sup>2<\/sup>+4<br \/>\n(iv) 1 + x<br \/>\n(v) 3t<br \/>\n(vi) r<sup>2<\/sup><br \/>\n(vii) 7x<sup>3<\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><br \/>\n<\/span><span style=\"color: #000000;\"><strong>Linear polynomial &#8211; <\/strong>A polynomial of degree one is called a linear polynomial.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Quadratic polynomial &#8211;<\/strong> A polynomial of degree two is called a quadratic polynomial.<br \/>\n<\/span><span style=\"color: #000000;\"><strong>Cubic polynomial &#8211;<\/strong> A polynomial of degree three is called a cubic polynomial.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) x<sup>2 <\/sup>+ x<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The highest power of x<sup>2 <\/sup>+ x is 2<br \/>\n<\/span><span style=\"color: #000000;\">The degree is 2.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, x<sup>2 <\/sup>+ x is a quadratic polynomial.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) x \u2013 x<sup>3<br \/>\n<\/sup><\/strong><\/span><span style=\"color: #000000;\">The highest power of x \u2013 x<sup>3\u00a0<\/sup>is 3.<br \/>\n<\/span><span style=\"color: #000000;\">The degree is 3.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, x \u2013 x<sup>3<\/sup>\u00a0is a cubic polynomial.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) y + y<sup>2 <\/sup>+ 4<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The highest power of y + y<sup>2 <\/sup>+ 4 is 2.<br \/>\n<\/span><span style=\"color: #000000;\">the degree is 2<br \/>\n<\/span><span style=\"color: #000000;\">Hence, y + y<sup>2 <\/sup>+ 4 is a quadratic polynomial<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) 1 + x<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The highest power of 1 + x is 1.<br \/>\n<\/span><span style=\"color: #000000;\">The degree is 1.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, 1 + x is a linear polynomial.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 3t<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The highest power of 3t is 1.<br \/>\n<\/span><span style=\"color: #000000;\">The degree is 1.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, 3t is a linear polynomial.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) r<sup>2<br \/>\n<\/sup><\/strong><\/span><span style=\"color: #000000;\">The highest power of r<sup>2\u00a0<\/sup>is 2.<br \/>\n<\/span><span style=\"color: #000000;\">The degree is 2.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, r<sup>2\u00a0<\/sup>is a quadratic polynomial.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vii) 7x<sup>3<br \/>\n<\/sup><\/strong><\/span><span style=\"color: #000000;\">The highest power of 7x<sup>3\u00a0<\/sup>is 3.<br \/>\n<\/span><span style=\"color: #000000;\">The degree is 3.<br \/>\n<\/span><span style=\"color: #000000;\">Hence, 7x<sup>3<\/sup>\u00a0is a cubic polynomial.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 2 (Polynomials)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 2 Polynomials Exercise 2.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 2: Polynomials\u00a0 NCERT Solution Class 9 Maths Ex &#8211; 2.2 NCERT Solution Class 9 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[703,702,186,704,701,5],"class_list":["post-4219","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-2-polynomials-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-2-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - 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