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


Transcript

Example 2 Check whether the following are quadratic equations: (i) (x – 2)2 + 1 = 2x – 3 (x – 2)2 + 1 = 2x – 3 Using (a – b)2 = a2 + b2 – 2ab (x2 + 4 – 4x) + 1 = 2x – 3 x2 + 5 – 4x = 2x – 3 x2 + 5 – 4x – 2x + 3 = 0 x2 – 6x + 8 = 0 It is the form ax2 + b x + c = 0 Where, a = 1, b = – 6, c = 8 Hence, it is a quadratic equation . Example 2 Check whether the following are quadratic equations: (ii) x(x + 1) + 8 = (x + 2) (x – 2) x (x + 1) + 8 = (x + 2) (x – 2) Using (a + b) (a – b) = a2 – b2 x (x + 1) + 8 = x2 – 4 x2 + x + 8 = x2 – 4 x2 + x + 8 – x2 + 4 = 0 (x2 – x2) + x + 8 + 4 = 0 x + 12 = 0 Since the highest power is 1 not 2 It is not in the form of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 =0 Hence, it is not a quadratic equation . Example 2 Check whether the following are quadratic equations: (iii) x (2x + 3) = x2 + 1 x(2x + 3) = x2 + 1 2x2 + 3x = x2 + 1 2x2 + 3x – x2 – 1 = 0 (2x2 – x2) + 3x – 1 = 0 x2 + 3x – 1 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = 3, c = – 1 Hence, it is a quadratic equation . Example 2 Check whether the following are quadratic equations: (iv) (x + 2)3 = x3 – 4 (x + 2)3 = x3 – 4 Using (a + b)3 = a3 + b3 + 3a2b + 3ab2 x3 + 23 + 3 (x2) (2) + 3 (x) (2)^2 = x3 – 4 x3 + 8 + 6x2 + 12x = x3 – 4 x3 + 8 + 6x2 + 12 x – x3 + 4 = 0 6x2 + 12x + 12 = 0 6(x2 + 2x + 2) = 0 x2 + 2x + 2 = 0 It is of the form ax2 + bx + c = 0 Where a = 1, b = 2, c = 2 Hence, it is 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.