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Question

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

A
6
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B
4
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C
9
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D
36
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Solution

The correct option is C 9
Consider the expression x2+6x.

x2+2×x×3

It is in the form of a2+2ab

By adding b2 we get the identity
a2+2ab+b2=(a+b)2 that represents a perfect square.

x2+2(x)(3)+32
=(x+3)2=x2+6x+9
is 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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