# For what value of n is x^2-11x+n a perfect square trinomial?

##### 1 Answer
Jul 1, 2015

If $n = \frac{121}{4}$ the ${x}^{2} - 11 x + n$ is a perfect square trinomial.

#### Explanation:

For a perfect square:
$\textcolor{w h i t e}{\text{XXXX}}$${\left(x - a\right)}^{2} = \textcolor{red}{{x}^{2} - 2 a x} + \textcolor{b l u e}{{a}^{2}}$

If $\textcolor{red}{{x}^{2} - 11 x}$ are the first two terms of such a perfect square
then $\textcolor{red}{2 a x} = \textcolor{red}{11 x}$
$\rightarrow \textcolor{red}{a} = \frac{11}{2}$
and (since we want $n$ to be the third term)
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{b l u e}{n} = \textcolor{b l u e}{{a}^{2}} = \frac{121}{4}$