Question

How do you find the value of K so each given trinomial is a perfect square? x^2+12x+k

Answer 1

36

Answer 2

how do you get that? :O

Answer 3

12/2 = 6

6^2 = 36

Answer 4

could i do the same with this 9x^2-10x+k ?

Answer 5

you can do it but you will not get an integer

Answer 6

you will get a fraction if you want a perfect square

Answer 7

the way you can make sure you have a perfect square is to make sure that
\[b^2-4ac=0\] so in this case you want
\[(-10)^2-4\times 9\times k=0\] or
\[100=36k\]
\[k=\frac{100}{36}=\frac{25}{9}\]

Answer 8

and then you will get
\[9x^2-10x+\frac{25}{9}=\frac{1}{9}(9x-5)^2\]

Answer 9

Oh I see, Thank you! :)