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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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 + 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 – 𝟏𝟎𝒙 – 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 + 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.