Check sibling questions

Ex 4.1, 1 - Check whether following are quadratic equations - Ex 4.1

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 2

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 3

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 4

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 5

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 6

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 7

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Ex 4.1, 1 - Chapter 4 Class 10 Quadratic Equations - Part 8

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Transcript

Ex 4.1 ,1 Check whether the following are quadratic equations : (i) (𝑥+1)^2 = 2(x – 3) (𝑥+1)^2 = 2(x – 3) 𝑥2+12+2×𝑥×1=2(𝑥−3) 𝑥2 + 1 + 2𝑥 = 2𝑥 – 6 𝑥2 + 1+ 2𝑥 – 2𝑥 + 6 = 0 𝑥2 + 1 +6 = 0 𝑥2 + 7 = 0 𝑥2 + 0𝑥 + 7 = 0 Since , it is of the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 =0 Where 𝑎 = 1, 𝑏 = 0, 𝑐 = 7 Hence, it is a quadratic equation Ex 4.1 ,1 Check whether the following are quadratic equations : (ii) x2 – 2x = (-2) (3 – x) x2 – 2x = (-2) (3 – x) x2 – 2x = (-2)3 – (–2)x x2 – 2x = –6 + 2x x2 – 2x – 2x + 6 = 0 x2 – 4x + 6 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = – 4 , c = 6 Hence, it is a quadratic equation . Ex 4.1 ,1 Check whether the following are quadratic equations : (iii) (x – 2)(x + 1) = (x – 1)(x + 3) (𝑥 – 2)(𝑥 + 1)= (𝑥 – 1)(𝑥 + 3) 𝑥 (𝑥 + 1) – 2 (𝑥 + 1) = 𝑥 (𝑥 + 3) – 1 (𝑥 + 3) 𝑥2 + 𝑥 – 2𝑥 – 2 = 𝑥2 + 3𝑥 – 𝑥 – 3 𝑥2 + 𝑥 – 2𝑥 – 2 – 𝑥2 – 3𝑥 + 𝑥 + 3 = 0 (𝑥2 – 𝑥2 ) + (𝑥 – 2𝑥 – 3𝑥 + 𝑥 ) – 2 + 3 = 0 0 – 3𝑥 + 1 = 0 – 3𝑥 + 1 = 0 Since , highest power is 1 not 2, It is not in the form of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 =0 Hence, it is not a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (iv) (x – 3)(2x +1) = x(x + 5) (𝑥 – 3) (2𝑥 + 1) = 𝑥 (𝑥 + 5) 𝑥 (2𝑥 + 1) – 3(2𝑥 + 1) = 𝑥 (𝑥 + 5) 2𝑥2 + 𝑥 – 6𝑥 −3 = 𝑥2 + 5𝑥 2𝑥2 + 𝑥 – 6𝑥 – 3 – 𝑥2 – 5𝑥 = 0 2𝑥2 – 𝑥2 +𝑥 – 6𝑥 – 5𝑥 – 3 = 0 𝑥2 – 10 𝑥 – 3 = 0 Since, the equation is of the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 Where, a = 1, b = – 10, c = – 3 Hence it is a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (v) (2x – 1)(x – 3) = (x + 5)(x – 1) (2𝑥 – 1)(𝑥 – 3)= (𝑥 + 5)(𝑥 – 1) 2𝑥 (𝑥 – 3) – 1 (𝑥 – 3) = 𝑥 (𝑥 – 1) + 5 (𝑥 – 1) 2𝑥2 – 6𝑥 – 𝑥 + 3 = 𝑥2 – 𝑥 + 5𝑥 – 5 2𝑥2 – 6𝑥 – 𝑥 + 3 – 𝑥2 + 𝑥 – 5𝑥 + 5 = 0 2𝑥2 – 𝑥2 – 6𝑥 – 𝑥 + 𝑥 – 5𝑥 + 3 + 5 = 0 𝑥2 – 11𝑥 + 8 = 0 Since it is of the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 =0 Where a = 1, b = – 11, c = 8 Hence it is a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (vi) x2 + 3x + 1 = (x – 2)2 𝑥2 + 3𝑥 + 1 = (𝑥 – 2)^2 𝑥2 + 3𝑥 +1 = 𝑥2+22−2 ×𝑥×2 𝑥2 +3𝑥 +1 = 𝑥2 + 4 – 4𝑥 𝑥2 + 3𝑥 + 1 – 𝑥2 – 4+ 4𝑥= 0 𝑥2 – 𝑥2 + 3𝑥 + 4𝑥 + 1 – 4 = 0 0 + 7𝑥 – 3 = 0 7𝑥 – 3 = 0 Since , highest power is 1 not 2, It is not in the form of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 =0 Hence, it is not a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (vii) (x + 2)3 = 2x (x2 – 1) (x + 2)3 = 2x (x2 – 1) x3 + 23 + 3 ×𝑥×2(𝑥+2)=2𝑥 (x2 – 1) 𝑥3 +8+6𝑥(𝑥+2)=2𝑥3−2𝑥 𝑥2 + 8 + 6𝑥2 + 12𝑥 = 2𝑥3 – 2𝑥 𝑥3 + 8 + 6𝑥2 + 12𝑥 – 2𝑥3 + 2𝑥 = 0 𝑥3 – 2𝑥3 + 6𝑥2 + 12𝑥 + 2𝑥 + 8 = 0 – 𝑥3 + 6𝑥2 +14𝑥 + 8 = 0 Since highest power is 3 and not 2, It is not in the form of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 =0 Hence, it is not a quadratic equation Ex 4.1 ,1 Check whether the following are quadratic equations : (viii) x3 – 4x2 – x + 1 = (x – 2)3 𝑥3 – 4𝑥2 – 𝑥+ 1 = (𝑥 – 2)^3 𝑥3 – 4𝑥2 – 𝑥+1 = 𝑥3 –23 −3×𝑥×2(x−2) 𝑥3 – 4𝑥2 – 𝑥+1 = 𝑥3 – 8 – 6𝑥 (𝑥 – 2) 𝑥3 – 4𝑥2 – 𝑥 +1 = 𝑥3 – 8 – 6𝑥2 + 12 𝑥 𝑥3 – 4𝑥2 – 𝑥 + 1 – 𝑥3 + 8 + 6𝑥2 – 12𝑥 = 0 𝑥3 – 𝑥3 – 4𝑥2 + 6𝑥2 – 𝑥 – 12𝑥 + 1 + 8 = 0 0 + 2𝑥2 – 13𝑥 + 9 = 0 2𝑥2 – 13𝑥 + 9 = 0 It is of the form ax2 + bx + c = 0 Where a = 2, b = – 13 and c = 9 Hence, it is a quadratic equation

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Davneet Singh

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.