Question

The number that is to be added to $x^2+2x$ to make the resultant a perfect square is .

• A. 2
• B. 3
• C. 1

Answer 1

The correct option is C 1

The identity $(a+b{)}^2=a^2+2ab+b^2$ represents a perfect square.
Consider the expression $x^2+2x.$ If we halve the coefficient of $x$ and add its square to this expression, we get
$x^2+2x+1.$
But, $x^2+2x+1=x^2+2\left(x\right)\left(1\right)+1^2$
$=(x+1{)}^2,$ a perfect square.
Thus, we have to add 1 to the expression $x^2+2x$ so that the resultant is a perfect square.