Factorise:

Question:

Factorise:

$z^{2}+z+\frac{1}{4}$

Solution:

We have:

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

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

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

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