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Example 1 (ii)
Example 2 Important You are here
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Example 5 Important
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Example 7 Deleted for CBSE Board 2023 Exams
Example 8 Important Deleted for CBSE Board 2023 Exams
Example 9 Important Deleted for CBSE Board 2023 Exams
Example 10
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Example 12 Important
Example 13 (i)
Example 13 (ii) Important
Example 13 (iii)
Example 14 (i)
Example 14 (ii)
Example 15 Important
Example 16
Example 17 Important
Example 18
Examples
Last updated at March 22, 2023 by Teachoo
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