InterviewSolution
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InterviewSolution
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Solve the quadratic equation by completing the square method.x2 + 2x – 5 = 0 |
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Answer» x2 + 2x – 5 = 0 If x2 + 2x + k = (x + a)2, then x2 + 2x + k = x2 + 2ax + a2 Comparing the coefficients, we get 2 = 2a and k = a2 ∴ a = 1 and k = (1)2 = 1 Now, x2 + 2x – 5 = 0 ∴ x2 + 2x + 1 – 1 – 5 = 0 ∴ (x + 1)2 – 6 = 0 ∴ (x + 1)2 = 6 Taking square root of both sides, we get x + 1 = ± √6 ∴ x + 1 √6 or x + 1 = √6 ∴ x = √6 – 1 or x = -√6 – 1 ∴ The roots of the given quadratic equation are √6 -1 and – √6 -1. |
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