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Example 2 - Check whether following are quadratic equations - Checking quadratic equation

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Example 2 - Chapter 4 Class 10 Quadratic Equations - Part 2

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Example 2 - Chapter 4 Class 10 Quadratic Equations - Part 3

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Example 2 - Chapter 4 Class 10 Quadratic Equations - Part 4

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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 2 + + =0 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.