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Question

The number that is to be added to x2+6x to make the resultant a perfect square is .

A
36
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B
18
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C
9
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D
72
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Solution

The correct option is C 9
The identity (a+b)2=a2+2ab+b2 represents a perfect square.
Consider the expression x2+6x. If we halve the coefficient of x and add its square to this expression, we get
x2+6x+9.
But, x2+6x+9=x2+2(x)(3)+32
=(x+3)2, a perfect square.
Thus, we have to add 9 to the expression x2+6x so that the resultant is a perfect square.

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