Question

The number to be added to make $x^2-\frac{1}{2}$ x a perfect square is

• A. $-\frac{1}{16}$
• B. $\frac{1}{4}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{16}$

Answer 1

The correct option is D $\frac{1}{16}$

$x^2-\frac{1}{2}x+\square =(x{)}^2-2(x)\left(\frac{1}{4}\right)+\square$
$=(x{)}^2-2(x)\left(\frac{1}{4}\right)+{\left(\frac{1}{4}\right)}^2=x^2-\frac{1}{2}x+\frac{1}{16}$
Therefore, 1/16 should be added.