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Chapter 2 Class 10 Polynomials
Serial order wise

For a linear polynomial kx + c, k โ‰  0, the graphย  of y = kx + c is a straight line which intersectsย  the X-axis at exactly one point, namely, ((-c)/k,0), Therefore, the linear polynomial kx + c, k โ‰  0, hasย  exactly one zero, namely, the X-coordinate of theย  point where the graph of y = kx + c intersects theย  X-axis.

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Question 1

If a linear polynomial is 2x + 3, then the zero ofย  2x + 3 is:

(a) 3/2ย 

(b) โˆ’ 3/2

(c) 2/3 ย ย 

(d) โˆ’ 2/3

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ย 

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Question 2

The graph of y = p(x) is given in figure below forย  some polynomial p(x). The number of zero/zeroesย  of p(x) is/are:

(a) 1ย 

(b) 2

(c) 3 ย  ย 

(d) 0

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Question 3

If ๐›ผ and ๐›ฝ are the zeroes of the quadratic polynomialย  x 2 โ€“ 5x + k such that ๐›ผ โ€“ ๐›ฝ = 1, then the value of k is:

(a) 4 ย 

(b) 5

(c) 6 ย 

(d) 3

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Question 4

If ฮฑ and ฮฒ are the zeroes of the quadratic polynomialย  p(x) = 4x2 + 5x + 1, then the product of zeroes is:

(a) โˆ’1 ย 

(b) 1/4

(c) โˆ’2 ย 

(d) โˆ’ 5/4

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Question 5

If the product of the zeroes of the quadraticย  polynomial p(x) = ax 2 โ€“ 6x โ€“ 6 is 4, then the valueย  of a is:

(a) โˆ’ 3/2 ย 

(b) 3/2

(c) 2/3 ย ย 

(d) โˆ’ 2/3

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Transcript

Question For a linear polynomial kx + c, k โ‰  0, the graph of y = kx + c is a straight line which intersects the X-axis at exactly one point, namely, ((โˆ’๐‘)/๐‘˜,0), Therefore, the linear polynomial kx + c, k โ‰  0, has exactly one zero, namely, the X-coordinate of the point where the graph of y = kx + c intersects the X-axis. Give answer the following questions: Question 1 If a linear polynomial is 2x + 3, then the zero of 2x + 3 is: (a) 3/2 (b) โˆ’ 3/2 (c) 2/3 (d) โˆ’ 2/3 Let p(x) = 2x + 3 Finding zero p(x) = 0 2x + 3 = 0 2x = โ€“ 3 x = (โˆ’๐Ÿ‘)/๐Ÿ So, the correct answer is (B) Question 2 The graph of y = p(x) is given in figure below for some polynomial p(x). The number of zero/zeroes of p(x) is/are: (a) 1 (b) 2 (c) 3 (d) 0 Number of zeroes is equal to number of times parabola intersects the x-axis Since the graph does not intersect the X-axis, โˆด Number of zeroes = 0 So, the correct answer is (d) Question 3 If ๐›ผ and ๐›ฝ are the zeroes of the quadratic polynomial x2 โ€“ 5x + k such that ๐›ผ โ€“ ๐›ฝ = 1, then the value of k is: (a) 4 (b) 5 (c) 6 (d) 3 Let p(x) = x2 โ€“ 5x + k Now, Sum of zeros = ๐’„/๐’‚ ๐›ผ + ๐›ฝ = (โˆ’(โˆ’5))/1 ๐›ผ + ๐›ฝ = 5 Also given, ๐œถ โˆ’ ๐œท = 1 Product of zeros = ๐’„/๐’‚ ๐›ผ๐›ฝ = ๐‘˜/1 ๐›ผ๐›ฝ = k Adding (1) and (2) ๐›ผ + ๐›ฝ + ๐›ผ โˆ’ ๐›ฝ = 5 + 1 2๐›ผ = 6 ๐›ผ = 6/2 ๐›ผ = 3 Putting ๐›ผ = 3 in (1) ๐›ผ + ๐›ฝ = 5 3 + ๐›ฝ = 5 ๐›ฝ = 5 โˆ’ 3 ๐›ฝ = 2 Now, from (3) ๐›ผ๐›ฝ = k 3 ร— 2 = k 6 = k k = 6 So, the correct answer is (C) Question 4 If ๐›ผ and ๐›ฝ are the zeroes of the quadratic polynomial p(x) = 4x2 + 5x + 1, then the product of zeroes is: (a) โˆ’1 (b) 1/4 (c) โˆ’2 (d) โˆ’ 5/4 Given p(x) = 4x2 + 5x + 1 Now, Product of Zeros = ๐‘/๐‘Ž = ๐Ÿ/๐Ÿ’ So, the correct answer is (B) Question 5 If the product of the zeroes of the quadratic polynomial p(x) = ax2 โ€“ 6x โ€“ 6 is 4, then the value of a is: (a) โˆ’ 3/2 (b) 3/2 (c) 2/3 (d) โˆ’ 2/3 Given p(x) = ax2 โ€“ 6x โ€“ 6 Here, Product of zeroes = ๐‘/๐‘Ž 4 = (โˆ’๐Ÿ”)/๐’‚ 4a = โˆ’6 a = (โˆ’6)/4 a = (โˆ’๐Ÿ‘)/๐Ÿ So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.