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Chapter 2 Class 10 Polynomials
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The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

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Question 1

In the standard form of quadratic polynomial, π‘Žπ‘₯ 2 +𝑏π‘₯+𝑐 Β 
a, b and c are
(a) All are real numbers Β 
(b) All are rational numbers.Β 
(c) β€˜a’ is a non zero real number and b and c are any real numbersΒ 
(d) All are integers

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Question 2

If the roots of the quadratic polynomial are equal, where the discriminant 𝐷=𝑏 2 βˆ’4π‘Žπ‘, then
(a) D > 0Β  (b) D < 0 Β  (c) D β‰₯ 0 Β  (d) D = 0 Β 

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Question 3

If a and 1/a are the zeroes of the quadratic polynomial 2π‘₯ 2 βˆ’ π‘₯ + 8π‘˜ then k is
(a) 4Β  (b) 1/4Β  (c) (-1)/4Β  Β  (d) 2

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Question 4

The graph of π‘₯ 2 +1=0
(a) Intersects x‐axis at two distinct points. Β 
(b) Touches x‐axis at a point. Β 
(c) Neither touches nor intersects x‐axis. Β 
(d) Either touches or intersects x‐ axis.

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Question 5

If the sum of the roots is –p and product of the roots is (-1)/p , then the quadratic polynomial is
(a) π‘˜(βˆ’π‘π‘₯ 2 +π‘₯/𝑝+1) Β (b) π‘˜(𝑝π‘₯ 2 βˆ’π‘₯/π‘βˆ’1) Β  Β 
(c) π‘˜(π‘₯ 2 +𝑝π‘₯βˆ’1/𝑝)Β  Β  (d) π‘˜(π‘₯ 2 βˆ’π‘π‘₯+1/𝑝)

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Transcript

Question The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.Question 1 In the standard form of quadratic polynomial, γ€–π‘Žπ‘₯γ€—^2+𝑏π‘₯+𝑐, a, b and c are (a) All are real numbers (b) All are rational numbers. (c) β€˜a’ is a non zero real number and b and c are any real numbers (d) All are integers For any quadratic polynomial γ€–π‘Žπ‘₯γ€—^2+𝑏π‘₯+𝑐 a β‰  0, and a, b, c are real numbers So, the correct answer is (C) Question 2 If the roots of the quadratic polynomial are equal, where the discriminant 𝐷=𝑏^2βˆ’4π‘Žπ‘, then (a) D > 0 (b) D < 0 (c) D β‰₯ 0 (d) D = 0 If Roots are equal D = 0 So, the correct answer is (D) Question 3 If π‘Ž and 1/π‘Ž are the zeroes of the quadratic polynomial 2π‘₯^2βˆ’π‘₯+8π‘˜ then k is (a) 4 (b) 1/4 (c) (βˆ’1)/4 (d) 2 Let p(x) = 2x2 βˆ’ x + 8k Since π‘Ž and 1/π‘Ž are the zeroes of p(x) Product of zeroes = π‘ͺ/𝑨 π‘Ž Γ— 1/π‘Ž = 8π‘˜/2 1 = 4 π‘˜ π‘˜ = 1/4 So, the correct answer is (B) Question 4 The graph of π‘₯^2+1=0 (a) Intersects x‐axis at two distinct points. (b) Touches x‐axis at a point. (c) Neither touches nor intersects x‐axis. (d) Either touches or intersects x‐ axis. The graph of π‘₯^2+1=0 looks like Thus, it neither touches nor intersects x‐axis. So, the correct answer is (c) Question 5 If the sum of the roots is –𝑝 and product of the roots is (βˆ’1)/𝑝 , then the quadratic polynomial is (a) π‘˜(βˆ’π‘π‘₯^2+π‘₯/𝑝+1) (b) π‘˜(𝑝π‘₯^2βˆ’π‘₯/π‘βˆ’1) (c) π‘˜(π‘₯^2+𝑝π‘₯βˆ’1/𝑝)" " (d) π‘˜(π‘₯^2βˆ’π‘π‘₯+1/𝑝)" " The quadratic polynomial is x2 βˆ’ (Sum of roots)x + Product of roots Putting values π‘₯^2+𝑝π‘₯+((βˆ’1)/𝑝) π‘₯^2+𝑝π‘₯βˆ’1/𝑝 We can multiply any constant to this polynomial So, required quadratic polynomial is π’Œ(𝒙^𝟐+π’‘π’™βˆ’πŸ/𝒑) So, the correct answer is (c)

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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.