Question

Factorise:
z² + z + $\frac{1}{4}$

Answer 1

We have:
$z^2+z+\frac{1}{4}=z^2+2\times z\times \frac{1}{2}\times {\left(\frac{1}{2}\right)}^2$
$={\left(z+\frac{1}{2}\right)}^2$

∴ $z^2+z+\frac{1}{4}={\left(z+\frac{1}{2}\right)}^2$