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

decide what number must be added to the binomial to make a perfect square x^2+(3/2)x

Caity from Boulder, CO 2/4/2013

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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

Kevin S. 2/4/2013

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