Solution:
A quadratic expression is said to be a perfect square trinomial if it has repeated factors.
Given the expression below:
[tex]x^2+7x+\frac{49}{4}[/tex]
By factorization, we have
[tex]\begin{gathered} (x^2+\frac{7}{2}x)+(\frac{7}{2}x+\frac{49}{4}) \\ factor\text{ out the common term,} \\ x(x+\frac{7}{2})+\frac{7}{2}(x+\frac{7}{2}) \\ This\text{ gives} \\ (x+\frac{7}{2})(x+\frac{7}{2}) \\ \Rightarrow(x+\frac{7}{2})^2 \\ \end{gathered}[/tex]
Since the above expression has a repeated factor of
[tex](x+\frac{7}{2})[/tex]
We can conclude that the expression is a perfect square trinomial.
