Polo's question at Yahoo Answers regarding making a perfect square trinomial

[MarkFL]

Here is the question:

Find the constant necessary to make a perfect square trinomial 5c^2-8c+__?

Here is a link to the question:

Find the constant necessary to make a perfect square trinomal 5c^2-8c+__? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Hello Polo,

Since the leading coefficient is 5, we may write a perfect square as follows:

\(\displaystyle \left(\sqrt{5}c+k \right)^2=5c^2+2\sqrt{5}kc+k^2\)

Now, we know by equating coefficients, that we require:

\(\displaystyle 2\sqrt{5}k=-8\,\therefore\,k=-\frac{4}{\sqrt{5}}\,\therefore\,k^2=\frac{16}{5}\)

Hence:

\(\displaystyle 5c^2-8c+\frac{16}{5}=\left(\sqrt{5}c-\frac{4}{\sqrt{5}} \right)^2\)

To Polo and any other guests viewing this topic, I invite and encourage you to post other algebra questions in our http://www.mathhelpboards.com/f2/ forum.

Best Regards,

Mark.

 

[agentredlum]

Nice , i like it especially because it's different than the 'normal' approach that dictates value of coefficient of x^2 must be 1 to 'complete' a square.

:)