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decide what number must be added to the binomial to make a perfect square

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1 Answer

The general form of a 2nd degree polynomial that is a perfect square is Ax2 + 2ACx + C2.

In this case, 2AC = 3/2. Since A = 1,
2C = 3/2 and C = 3/4

So the number that needs to be added is C2 = (3/4)2 = 9/16

and our polynomial is x2+ (3/2)x + 9/16