{"id":623918,"date":"2023-09-01T01:20:27","date_gmt":"2023-09-01T01:20:27","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=623918"},"modified":"2023-09-01T02:35:36","modified_gmt":"2023-09-01T02:35:36","slug":"kc-sinha-exercise-2-1-mathematics-solution-class-10-chapter-2-real-numbers","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-2-1-mathematics-solution-class-10-chapter-2-real-numbers\/","title":{"rendered":"KC Sinha: Exercise 2.1 – Mathematics Solution Class 10 Chapter 2 Real numbers"},"content":{"rendered":"\n\n\n\n\n

Question 1 <\/h4>\n\n\n\n

Examine, seeing the graph of the polynomials given below, whether they are a linear or quadratic polynomial or neither linear nor quadratic polynomial:<\/strong><\/p>\n\n\n\n

(i)<\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(i)<\/strong> In general, we know that for a linear polynomial ax + b, a\u22600, the graph of y = ax + b is a straight line which intersects the x \u2013 axis at exactly one point.
And here, we can see that the graph of y = p(x) is a straight line and intersects the x \u2013 axis at exactly one point. Therefore, the given graph is of a Linear Polynomial.<\/strong><\/p>\n\n\n\n

(ii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(ii) Here, the graph of y = p(x) is a straight line and parallel to the x \u2013 axis . Therefore, the given graph is of a Linear Polynomial.<\/strong><\/p>\n\n\n\n

(iii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(iii) For any quadratic polynomial ax2<\/sup> + bx + c, a \u2260 0, the graph of the corresponding equation y = a x2<\/sup> + bx + c has one of the two shapes either open upwards like<\/a>or open downwards like<\/a>depending on whether a > 0 or a < 0. (These curves are called parabolas.)
Here, we can see that the shape of the graph is a parabola. Therefore, the given graph is of a Quadratic Polynomial.<\/strong><\/p>\n\n\n\n

(iv) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

<\/strong><\/p>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(iv) For any quadratic polynomial ax2<\/sup> + bx + c, a \u2260 0, the graph of the corresponding equation y = ax2<\/sup> + bx + c has one of the two shapes either open upwards like <\/a>or open downwards like<\/a> depending on whether a > 0or a < 0. (These curves are called parabolas.)
Here, we can see that the shape of the graph is parabola. Therefore, the given graph is of a Quadratic Polynomial.<\/strong><\/p>\n\n\n\n

(v) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(v) The shape of the graph is neither a straight line nor a parabola. So, the graph is not of a linear polynomial nor a quadratic polynomial.<\/p>\n\n\n\n

(vi) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(vi) The given graph have a straight line but it doesn\u2019t intersect at x \u2013 axis and the shape of the graph is also not a parabola. So, it is not a graph of a quadratic polynomial. Therefore, it is not a graph of linear polynomial or quadratic polynomial.<\/p>\n\n\n\n

(vii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(vii) The shape of the graph is neither a straight line nor a parabola. So, the graph is not of a linear polynomial or a quadratic polynomial.<\/p>\n\n\n\n

(viii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :
(viii) The shape of the graph is neither a straight line nor a parabola. So, the graph is not of a linear polynomial or a quadratic polynomial.<\/p>\n\n\n\n

\n\n\n\n

Question 2 <\/h4>\n\n\n\n

The graphs of y \u2013 p(x) are given in the figures below, where p(x) is a polynomial. Find the number of zeros in each case.<\/strong><\/p>\n\n\n\n

(i) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(i) Here, the graph of y = p(x) intersects the x \u2013 axis at two points. So, the number of zeroes is 2.<\/p>\n\n\n\n

(ii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(ii) Here, the graph of y = p(x) intersects the x \u2013 axis at three points. So, the number of zeroes is 3.<\/p>\n\n\n\n

(iii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(iii) Here, the graph of y = p(x) intersects the x \u2013 axis at one point only. So, the number of zeroes is 1.<\/p>\n\n\n\n

(iv) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(iv) Here, the graph of y = p(x) intersects the x \u2013 axis at exactly one point. So, the number of zeroes is 1.<\/p>\n\n\n\n

(v) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/strong><\/p>\n\n\n\n

(v) Here, the graph of y = p(x) intersects the x \u2013 axis at two points. So, the number of zeroes is 2.<\/p>\n\n\n\n

(vi) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :
(vi) Here, the graph of y = p(x) intersects the x \u2013 axis at exactly one point. So, the number of zeroes is 1.<\/p>\n\n\n\n

\n\n\n\n

Question 3 <\/h4>\n\n\n\n

The graphs of y = p(x) are given in the figures below, where p(x) is a polynomial Find the number of zeroes in each case.<\/strong><\/p>\n\n\n\n

(i) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :
(i) Here, the graph of y = p(x) intersect the x \u2013 axis at zero points. So, the number of zeroes is 0.
<\/p>\n\n\n\n

(ii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/p>\n\n\n\n

(ii) Here, the graph of y = p(x) intersects the x \u2013 axis at two points. So, the number of zeroes is 2.
<\/p>\n\n\n\n

(iii) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/p>\n\n\n\n

(iii) Here, the graph of y = p(x) intersects the x \u2013 axis at four points. So, the number of zeroes is 4.
<\/p>\n\n\n\n

(iv) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/p>\n\n\n\n

(iv) Here, the graph of y = p(x) does not intersects the x \u2013 axis. So, the number of zeroes is 0.
<\/p>\n\n\n\n

(v) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/p>\n\n\n\n

(v) Here, the graph of y = p(x) intersects the x \u2013 axis at two points. So, the number of zeroes is 2.
<\/p>\n\n\n\n

(vi) <\/strong><\/p>\n\n\n\n

\"\"\/<\/a><\/figure>\n\n\n\n

Sol :<\/p>\n\n\n\n

(vi) Here, the graph of y = p(x) intersects the x \u2013 axis at two points. So, the number of zeroes is 2.<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 10 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Question 1  Examine, seeing the graph of the polynomials given below, whether they are a linear or quadratic polynomial or neither linear nor quadratic polynomial: (i) Sol : (i) In general, we know that for a linear polynomial ax + b, a\u22600, the graph of y = ax + b is a straight line which intersects the […]<\/p>\n","protected":false},"author":302,"featured_media":623922,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[24],"tags":[],"boards":[],"class_list":["post-623918","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10","entry"],"yoast_head":"\nKC Sinha: Exercise 2.1 - Mathematics Solution Class 10 Chapter 2 Real numbers - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"Question 1  Examine, seeing the graph of the polynomials given below, whether they are a linear or quadratic polynomial or neither linear nor\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-2-1-mathematics-solution-class-10-chapter-2-real-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 2.1 - 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