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Write x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers. (A) (x − 4)2 = 3 (B) (x − 3)2 = 2 (C) (x − 2)2 = 1 (D)(x − 1)2 = 4

Ronald Miller

in Mathematics

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Brandon Scott on March 23, 2018

This is the so-called completing the square method, and in order to carry out this method, you must follow certain steps. The first step is to make sure that the value of the coefficient of x^2 is 1, that is. Then, we will divide the second term, 2x in this case, by 2x. In this case, the ratio comes to be 1. Now, we add the square of the ratio of both sides of the equation to get x^2 - 2x + 1 - 3 = 1. Then, we will implement the completion of the square formula to get (x - 1)^2 - 3 = 1. The change of this in the required form, (x - 1)^2 = 4. The value of a is 1 and the value of b is 4. The answer is D.


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