anonymous 4 years ago State the value of k that makes each expression a perfect square trinomial. Then, write the trinomial as the square of a binomial: p^2 - 5p + k.

1. Hero

p^2 - 5p + 25/4 (p - 5/2)^2

2. anonymous

why is it 25/4...?

3. anonymous

the answer is supposed to be: 6.25

4. anonymous

i believe they are the same number

5. anonymous

it is the answer but why is it 25/4?

6. anonymous

it is $\frac{25}{4}$ because $(\frac{5}{2})^2=\frac{25}{4}$

7. anonymous

ohhhhh

8. anonymous

and it is $\frac{5}{2}$ because you started with $x^2-5x+k$

9. anonymous

ohh, i get it now thank you!

10. anonymous

Okay so here's what I did: $p ^{2} - 5p + k =0$ coefficient of p = -5 coefficient of p / 2 = -5/2 (coefficient of p/2)^2 = (-5/2)^2 = 25.4 $p ^{2} - 5p + 25/4 = -k + \left(\begin{matrix}25 \\ 4\end{matrix}\right)$

11. anonymous

= $(p - 5/2)^{2} = -25/4$ = $p - 5/2 = +- (\sqrt{25}/\sqrt{4}$

12. anonymous

p = -5/3 +- 5/2 Help!